# Physics Research Papers

Since 2009, the * Journal of Physics A* has awarded a Best Paper Prize, which serves to celebrate well written papers that make significant contributions to their fields.

We welcome your nominations for the 2018 Best Paper Prize. Up to three prizes worth £250 will be awarded. All original research articles published in the journal during 2016 and 2017 can be considered for a prize and the nominations will be judged by our Section Editors using the criteria of novelty, achievement, potential impact and presentation.

If you wish to make a nomination for the Best Paper Prize, please send an email to our editorial office (jphysa@iop.org) giving the publication details of the paper and stating (in no more than 1000 words) how it meets the criteria listed above. Authors cannot nominate their own papers. The closing date for nominations is **31 March 2018**. Please note that topical review articles are not eligible for the best paper prize.

We look forward to receiving your nominations. For further information please contact the editorial office (jphysa@iop.org).

**Martin EvansEditor-in-Chief**

**Rebecca GillanExecutive Editor**

### Past winners of the Best Paper Prize

#### 2017

#### 2016

Read interviews with our winners here:

David Gómez-Ullate, Yves Grandati and Robert Milson

Timothy J Hollowood, J Luis Miramontes and David M Schmidtt

Jesper Lykke Jacobsen

#### 2015

#### 2014

#### 2013

#### 2012

#### 2011

#### 2010

#### 2009

_{d},

*F*-theorem and the expansion

Simone Giombi *et al* 2016 *J. Phys. A: Math. Theor.***49** 135403

View abstractView articlePDF

We calculate the free energies *F* for *U*(1) gauge theories on the *d* dimensional sphere of radius *R*. For the theory with free Maxwell action we find the exact result as a function of *d*; it contains the term consistent with the lack of conformal invariance in dimensions other than 4. When the *U*(1) gauge theory is coupled to a sufficient number *N*_{f} of massless four-component fermions, it acquires an interacting conformal phase, which in describes the long distance behavior of the model. The conformal phase can be studied using large *N*_{f} methods. Generalizing the *d* = 3 calculation in arXiv: 1112.5342, we compute its sphere free energy as a function of *d*, ignoring the terms of order and higher. For finite *N*_{f} , following arXiv: 1409.1937 and arXiv: 1507.01960, we develop the expansion for the sphere free energy of conformal QED _{d} . Its extrapolation to *d* = 3 shows very good agreement with the large *N*_{f} approximation for . For *N*_{f} at or below some critical value , the symmetric conformal phase of QED _{3} is expected to disappear or become unstable. By using the *F*-theorem and comparing the sphere free energies in the conformal and broken symmetry phases, we show that . As another application of our results, we calculate the one loop beta function in conformal QED _{6}, where the gauge field has a four-derivative kinetic term. We show that this theory coupled to *N*_{f} massless fermions is asymptotically free.

https://doi.org/10.1088/1751-8113/49/13/135403Cited byReferences

Silvio Franz and Giorgio Parisi 2016 *J. Phys. A: Math. Theor.***49** 145001

View abstractView articlePDF

We study a well known neural network model—the perceptron—as a simple statistical physics model of jamming of hard objects. We exhibit two regimes: (1) a convex optimization regime where jamming is hypostatic and non-critical; (2) a non-convex optimization regime where jamming is isostatic and critical. We characterize the critical jamming phase through exponents describing the distribution laws of forces and gaps. Surprisingly we find that these exponents coincide with the corresponding ones recently computed in high dimensional hard spheres. In addition, modifying the perceptron to a random linear programming problem, we show that isostaticity is not a sufficient condition for singular force and gap distributions. For that, fragmentation of the space of solutions (replica symmetry breaking) appears to be a crucial ingredient. We hypothesize universality for a large class of non-convex constrained satisfaction problems with continuous variables.

https://doi.org/10.1088/1751-8113/49/14/145001Cited byReferences

David Gómez-Ullate *et al* 2014 *J. Phys. A: Math. Theor.***47** 015203

View abstractView articlePDF

We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of state-deleting Darboux transformations on the harmonic oscillator. Equivalently, every exceptional orthogonal polynomial system of Hermite type can be obtained by applying a Darboux–Crum transformation to the classical Hermite polynomials. Exceptional Hermite polynomial systems only exist for even codimension 2 *m*, and they are indexed by the partitions λ of *m*. We provide explicit expressions for their corresponding orthogonality weights and differential operators and a separate proof of their completeness. Exceptional Hermite polynomials satisfy a 2ℓ + 3 recurrence relation where ℓ is the length of the partition λ. Explicit expressions for such recurrence relations are given.

https://doi.org/10.1088/1751-8113/47/1/015203Cited byReferences

Jesper Lykke Jacobsen 2014 *J. Phys. A: Math. Theor.***47** 135001

View abstractView articlePDF

The critical curves of the *q*-state Potts model can be determined exactly for regular two-dimensional lattices *G* that are of the three-terminal type. This comprises the square, triangular, hexagonal and bow–tie lattices. Jacobsen and Scullard have defined a graph polynomial *P _{B}*(

*q*,

*v*) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis

*B*, and its real roots in the temperature variable

*v*= e

^{K}− 1 provide increasingly accurate approximations to the critical manifolds upon increasing the size of

*B*. Using transfer matrix techniques, these authors computed

*P*(

_{B}*q*,

*v*) for large bases (up to 243 edges), obtaining determinations of the ferromagnetic critical point

*v*

_{c}> 0 for the (4, 8

^{2}), kagome, and (3, 12

^{2}) lattices to a precision (of the order 10

^{−8}) slightly superior to that of the best available Monte Carlo simulations. In this paper we describe a more efficient transfer matrix approach to the computation of

*P*(

_{B}*q*,

*v*) that relies on a formulation within the periodic Temperley–Lieb algebra. This makes possible computations for substantially larger bases (up to 882 edges), and the precision on

*v*

_{c}is hence taken to the range 10

^{−13}. We further show that a large variety of regular lattices can be cast in a form suitable for this approach. This includes all Archimedean lattices, their duals and their medials. For all these lattices we tabulate high-precision estimates of the bond percolation thresholds

*p*

_{c}and Potts critical points

*v*

_{c}. We also trace and discuss the full Potts critical manifold in the (

*q*,

*v*) plane, paying special attention to the antiferromagnetic region

*v*< 0. Finally, we adapt the technique to site percolation as well, and compute the polynomials

*P*(

_{B}*p*) for certain Archimedean and dual lattices (those having only cubic and quartic vertices), using very large bases (up to 243 vertices). This produces the site percolation thresholds

*p*

_{c}to a precision of the order of 10

^{−9}.

https://doi.org/10.1088/1751-8113/47/13/135001Cited byReferences

_{5}

**×**

*S*

^{5}superstring

Timothy J Hollowood *et al* 2014 *J. Phys. A: Math. Theor.***47** 495402

View abstractView articlePDF

The *S*-matrix on the world-sheet theory of the string in AdS has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where *q* is real has been identified as a particular deformation of the Green–Schwarz sigma model. An interpretation of the case with *q* a root of unity has, until now, been lacking. We show that the Green–Schwarz sigma model admits a discrete deformation which can be viewed as a rather simple deformation of the gauged WZW model, where . The deformation parameter *q* is then a *k*th root of unity where *k* is the level. The deformed theory has the same equations-of-motion as the Green–Schwarz sigma model but has a different symplectic structure. We show that the resulting theory is integrable and has just the right amount of kappa-symmetries that appear as a remnant of the fermionic part of the original gauge symmetry. This points to the existence of a fully consistent deformed string background.

https://doi.org/10.1088/1751-8113/47/49/495402Cited byReferences

Juan Maldacena and Alexander Zhiboedov 2013 *J. Phys. A: Math. Theor.***46** 214011

View abstractView articlePDF

We study the constraints imposed by the existence of a single higher spin conserved current on a three-dimensional conformal field theory (CFT). A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of *N* free bosons or free fermions. This is an extension of the Coleman–Mandula theorem to CFT’s, which do not have a conventional S-matrix. We also briefly discuss the case where the higher spin symmetries are ‘slightly’ broken.

This article is part of a special issue of *Journal of Physics A: Mathematical and Theoretical* devoted to ‘Higher spin theories and holography’.

https://doi.org/10.1088/1751-8113/46/21/214011Cited byReferences

John Cardy 2013 *J. Phys. A: Math. Theor.***46** 285402

View abstractView articlePDF

We consider the mutual Rényi information of disjoint compact spatial regions *A* and *B* in the ground state of a *d* + 1-dimensional conformal field theory (CFT), in the limit when the separation *r* between *A* and *B* is much greater than their sizes *R*_{A, B}. We show that in general , where α is the smallest sum of the scaling dimensions of operators whose product has the quantum numbers of the vacuum, and the constants depend only on the shape of the regions and universal data of the CFT. For a free massless scalar field, where α = *d* − 1, we show that is proportional to the capacitance of a thin conducting slab in the shape of *A* in *d* + 1-dimensional electrostatics, and give explicit formulae for this when *A* is the interior of a sphere *S*^{d − 1} or an ellipsoid. For spherical regions in *d* = 2 and 3 we obtain explicit results for *C*^{( n)} for all *n* and hence for the leading term in the mutual information by taking *n* → 1. We also compute a universal logarithmic correction to the area law for the Rényi entropies of a single spherical region for a scalar field theory with a small mass.

https://doi.org/10.1088/1751-8113/46/28/285402Cited byReferences

David S Dean *et al* 2014 *J. Phys. A: Math. Theor.***47** 372001

View abstractView articlePDF

M McKague *et al* 2012 *J. Phys. A: Math. Theor.***45** 455304

View abstractView articlePDF

In this paper, we introduce a general framework to study the concept of robust self-testing which can be used to self-test maximally entangled pairs of qubits (EPR pairs) and local measurement operators. The result is based only on probabilities obtained from the experiment, with tolerance to experimental errors. In particular, we show that if the results of an experiment approach the Cirel'son bound, or approximate the Mayers–Yao-type correlations, then the experiment must contain an approximate EPR pair. More specifically, there exist local bases in which the physical state is close to an EPR pair, possibly encoded in a larger environment or ancilla. Moreover, in these bases the measurements are close to the qubit operators used to achieve the Cirel'son bound or the Mayers–Yao results.

https://doi.org/10.1088/1751-8113/45/45/455304Cited byReferences

M A Vasiliev 2013 *J. Phys. A: Math. Theor.***46** 214013

View abstractView articlePDF

Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the AdS _{4} higher spin gauge theory shown to be dual to the theory of 3 *d* conformal currents of all spins interacting with 3 *d* conformal higher spin fields of Chern–Simons type. Generally, the resulting 3 *d* boundary conformal theory is nonlinear, providing an interacting version of the 3 *d* boundary sigma model conjectured by Klebanov and Polyakov to be dual to the AdS _{4} higher spin theory in the large *N* limit. Being a gauge theory, it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3 *d* boundary conformal theory to be free. Two reductions of particular higher spin gauge theories where boundary higher spin gauge fields decouple from the currents and which have free-boundary duals are identified. Higher spin holographic duality is also discussed for the cases of AdS _{3}/CFT _{2} and duality between higher spin theories and nonrelativistic quantum mechanics. In the latter case, it is shown in particular that (dS) AdS geometry in the higher spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup.

This article is part of a special issue of *Journal of Physics A: Mathematical and Theoretical* devoted to ‘Higher spin theories and holography’.

https://doi.org/10.1088/1751-8113/46/21/214013Cited byReferences

S V Manakov and P M Santini 2011 *J. Phys. A: Math. Theor.***44** 345203

View abstractView articlePDF

We have recently solved the inverse spectral problem for integrable partial differential equations (PDEs) in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter λ. The associated inverse problem, in particular, can be formulated as a nonlinear Riemann–Hilbert (NRH) problem on a given contour of the complex λ plane. The most distinguished examples of integrable PDEs of this type, like the dispersionless Kadomtsev–Petviashivili (dKP), the heavenly and the two-dimensional dispersionless Toda equations, are real PDEs associated with Hamiltonian vector fields. The corresponding NRH data satisfy suitable reality and symplectic constraints. In this paper, generalizing the examples of solvable NRH problems illustrated in Manakov and Santini ( 2009 *J. Phys. A: Math. Theor.***42** 095203; 2008 *J. Phys. A: Math. Theor.***41** 055204; 2009 *J. Phys. A: Math. Theor*. **42** 404013), we present a general procedure to construct solvable NRH problems for integrable real PDEs associated with Hamiltonian vector fields, allowing one to construct exact implicit solutions of such PDEs parametrized by an arbitrary number of real functions of a single variable. Then, we illustrate this theory on few distinguished examples for the dKP and heavenly equations. For the dKP case, we characterize a class of similarity solutions, of solutions constant on their parabolic wave front and breaking simultaneously on it, of localized solutions whose breaking point travels with constant speed along the wave front, and of localized solutions breaking in a point of the ( *x*, *y*) plane. For the heavenly equation, we characterize two classes of symmetry reductions.

https://doi.org/10.1088/1751-8113/44/34/345203Cited byReferences

_{5}

Lionel Mason and David Skinner 2011 *J. Phys. A: Math. Theor.***44** 135401

View abstractView articlePDF

We show that one-loop scalar box functions can be interpreted as volumes of geodesic tetrahedra embedded in a copy of AdS _{5} that has dual conformal spacetime as boundary. When the tetrahedron is space-like, it lies in a totally geodesic hyperbolic three-space inside AdS _{5}, with its four vertices on the boundary. It is a classical result that the volume of such a tetrahedron is given by the Bloch–Wigner dilogarithm. We show that this agrees with the standard physics formulae for such box functions. The combinations of box functions that arise in the *n*-particle one-loop MHV amplitude in super Yang–Mills correspond to the volume of a three-dimensional polytope without boundary, all of whose vertices are attached to a null polygon (which in other formulations is interpreted as a Wilson loop) at infinity.

https://doi.org/10.1088/1751-8113/44/13/135401Cited byReferences

Gaëtan Borot and Céline Nadal 2012 *J. Phys. A: Math. Theor.***45** 075209

View abstractView articlePDF

We compute the distribution of the purity for random density matrices (i.e. random mixed states) in a large quantum system, distributed according to the Bures measure. The full distribution of the purity is computed using a mapping to random matrix theory and then a Coulomb gas method. We find three regimes that correspond to two phase transitions in the associated Coulomb gas. The first transition is characterized by an explosion of the third derivative on the left of the transition point. The second transition is of first order, it is characterized by the detachment of a single charge of the Coulomb gas. A key remark in this paper is that the random Bures states are closely related to the *O*( *n*) model for *n* = 1. This actually led us to study ‘generalized Bures states’ by keeping *n* general instead of specializing to *n* = 1.

https://doi.org/10.1088/1751-8113/45/7/075209Cited byReferences

*N*th-order symmetries in classical and quantum mechanics

E G Kalnins *et al* 2010 *J. Phys. A: Math. Theor.***43** 035202

View abstractView articlePDF

We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.

https://doi.org/10.1088/1751-8113/43/3/035202Cited byReferences

*Y*-system for scattering amplitudes

Luis F Alday *et al* 2010 *J. Phys. A: Math. Theor.***43** 485401

View abstractView articlePDF

We compute super Yang–Mills planar amplitudes at strong coupling by considering minimal surfaces in AdS _{5} space. The surfaces end on a null polygonal contour at the boundary of AdS. We show how to compute the area of the surfaces as a function of the conformal cross ratios characterizing the polygon at the boundary. We reduce the problem to a simple set of functional equations for the cross ratios as functions of the spectral parameter. These equations have the form of thermodynamic Bethe ansatz (TBA) equations. The area is the free energy of the TBA system. We consider any number of gluons and in any kinematic configuration.

https://doi.org/10.1088/1751-8113/43/48/485401Cited byReferences

Jérôme Dubail *et al* 2010 *J. Phys. A: Math. Theor.***43** 482002

View abstractView articlePDF

We address the geometrical critical behavior of the two-dimensional *Q*-state Potts model in terms of the spin clusters (i.e. connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin–Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when *Q* is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents , valid for 0 ≤ *Q* ≤ 4, that describe the insertion of ℓ _{1} thin and ℓ _{2} thick domain walls.

https://doi.org/10.1088/1751-8113/43/48/482002Cited byReferences

*N*= 4 SUSY

L N Lipatov 2009 *J. Phys. A: Math. Theor.***42** 304020

View abstractView articlePDF

We argue that the multi-particle scattering amplitudes in *N* = 4 SUSY at large *N _{c}* and in the multi-Regge kinematics for some physical regions have the high energy behavior corresponding to the contribution of the Mandelstam cuts in the corresponding

*t*-channel partial waves. The Mandelstam cuts correspond to gluon composite states in the adjoint representation of the gauge group

*SU*(

*N*). The Hamiltonian for these states in the leading logarithmic approximation coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wavefunctions using the integrals of motion and the Baxter–Sklyanin approach.

_{c}https://doi.org/10.1088/1751-8113/42/30/304020Cited byReferences

Ram Band *et al* 2009 *J. Phys. A: Math. Theor.***42** 175202

View abstractView articlePDF

We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns techniques of assembly which are both stated generally and demonstrated. For this purpose, quantum graphs are grist to the mill. We develop the intuition that stands behind the construction as well as the practical skills of producing isospectral objects. We discuss the theoretical implications which include Sunada's theorem of isospectrality (Sunada 1985 *Ann. Math.***121** 169) arising as a particular case of this method. A gallery of new isospectral examples is presented, and some known examples are shown to result from our theory.

https://doi.org/10.1088/1751-8113/42/17/175202Cited byReferences

Alexander G Abanov *et al* 2009 *J. Phys. A: Math. Theor.***42** 135201

View abstractView articlePDF

We develop a hydrodynamic description of the classical Calogero–Sutherland liquid: a Calogero–Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin–Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin–Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin–Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin–Ono equations and of the chiral nonlinear equations.

https://doi.org/10.1088/1751-8113/42/13/135201Cited byReferences

Julien Tailleur *et al* 2008 *J. Phys. A: Math. Theor.***41** 505001

View abstractView articlePDF

Systems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out-of-equilibrium systems. The evolution of coarse-grained variables is governed by stochastic *hydrodynamic* equations in the limit of small noise. As such it is amenable to a treatment formally equal to the semiclassical limit of quantum mechanics, which reduces the problem of finding the full distribution functions to the solution of a set of Hamiltonian equations. It is in general not possible to solve such equations explicitly, but for an interesting set of problems (the driven symmetric exclusion process and the Kipnis–Marchioro–Presutti model) it can be done by a sequence of remarkable changes of variables. We show that at the bottom of this 'miracle' is the surprising fact that these models can be taken through a non-local transformation into isolated systems satisfying detailed balance, with probability distribution given by the Gibbs–Boltzmann measure. This procedure can in fact also be used to obtain an elegant solution of the much simpler problem of non-interacting particles diffusing in a one-dimensional potential, again using a transformation that maps the driven problem into an undriven one.

https://doi.org/10.1088/1751-8113/41/50/505001Cited byReferences

_{5}

**×**

*S*

^{5}superstring

Gleb Arutyunov *et al* 2007 *J. Phys. A: Math. Theor.***40** 3583

View abstractView articlePDF

We analyse the supersymmetry algebra of a superstring propagating in the AdS _{5} × S ^{5} background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We focus on the subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is expressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic *S*-matrix in the dual gauge theory.

https://doi.org/10.1088/1751-8113/40/13/018Cited byReferences

* Results in Physics* is an open access journal offering authors the opportunity to publish in

**all fundamental and interdisciplinary areas**of

**physics**,

**materials science**, and

**applied physics**. Papers of a

**theoretical**,

**computational**, and

**experimental nature**are all welcome.

*Results in Physics*accepts papers that are

**scientifically sound**,

**technically correct**and provide valuable new knowledge to the physics community. Topics such as three-dimensional flow and magnetohydrodynamics are not within the scope of

*Results in Physics*.

*Results in Physics* welcomes two types of papers:

1. **Full research papers**

2. **Microarticles**: very **short** papers, no longer than **two pages**. They may consist of a **single, but well-described piece of information**, such as:

- **Data** and/or a **plot** plus a **description**

- Description of a new **method** or **instrumentation**

- **Negative results**

- **Concept** or **design study**

All submitted manuscripts are fully peer-reviewed and after acceptance, a publication fee is charged to cover all editorial, production, and archiving costs. Different publication fees apply for the two types of papers: USD 850 for full papers and USD 550 for microarticles (excluding taxes). Accepted papers are freely accessible to anyone.

Hide full Aims & Scope