Chiral symmetry,the 1/N expansion and the SU(N) thirring model

In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, $\text{〈}\text{ψ}\text{ψ(x)}\text{ψ}\text{ψ(0)〉}$ vanishes in this model as |x|^?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.     

Magnetic order in the two-dimensional compass-Heisenberg model

A Green-function theory for the dynamic spin susceptibility in the square-latticespin-1/2 antiferromagneticcompass-Heisenberg model employing a generalized mean-field approximation is presented.The theory describes magnetic long-range order (LRO) and short-range order (SRO) atarbitrary temperatures. The magnetization, Néel temperature T _N , specific heat, anduniform static spin susceptibility χ are calculated self-consistently. As the mainresult, we obtain LRO at finite temperatures in two dimensions, where the dependence ofT _N on the compass-modelinteraction is studied. We find that T _N is close to theexperimental value for Ba₂IrO₄. The effects of SRO are discussed in relation to thetemperature dependence of χ.     

Two-dimensional Brownian vortices

We introduce a stochastic model of 2D Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other (“plasma” case) and at negative temperatures, like-sign vortices attract each other (“gravity” case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N-body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N, where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for N→+∞. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-Hückel approximation valid at the order O(1/N). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-Hückel model of electrolytes.     

The interaction of nucleons with antinucleons. III. Photon and pion emission from bound states

We calculate widths and branching ratios for the emission of γ rays or pions from a bound state of the nucleon-antinucleon ($\text{N}\text{N}$) system, leading to another $\text{N}\text{N}$ bound state. We use a realistic potential model to describe the medium- and long-range parts of the $\text{N}\text{N}$ interaction, and parametrize the short-range behavior. The general features of γ and π transitions, based on the selection rules, are emphasized. We illustrate these features with typical results for several choices of the short-range cutoff. The observation of pions is a necessary supplement to the γ-ray experiments, in order to significantly constrain the possible quantum number assignments of final states. We investigate transitions between quasiatomic (QA) and more deeply bound quasinuclear (QN) states, and also QN to QN γ or π emission. The former may have been seen in experiments involving the $\text{p}\text{p}$ atom, while the latter are in some optimum cases accessible in $\text{p}\text{d}$ spectator experiments, although there is no evidence for these QN to QN transitions as yet. The role of isospin mixing in QA states is discussed, as well as the importance of maintaining orthogonality of the QA and QN wave functions.     

Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System

We study a system of rods onℤ², with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N = 2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.     

Hamiltonian and Brownian systems with long-range interactions: III. The BBGKY hierarchy for spatially inhomogeneous systems

We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in powers of 1/N in a proper thermodynamic limit N→+∞, where N is the number of particles. These correlations are responsible for the “collisional” evolution of the system beyond the Vlasov regime due to finite N effects. We obtain a general kinetic equation that can be applied to spatially inhomogeneous systems and that takes into account memory effects. These peculiarities are specific to systems with unshielded long-range interactions. For spatially homogeneous systems with short memory time like plasmas, we recover the classical Landau (or Lenard-Balescu) equations. An interest of our approach is to develop a formalism that remains in physical space (instead of Fourier space) and that can deal with spatially inhomogeneous systems. This enlightens the basic physics and provides novel kinetic equations with a clear physical interpretation. However, unless we restrict ourselves to spatially homogeneous systems, closed kinetic equations can be obtained only if we ignore some collective effects between particles. General exact coupled equations taking into account collective effects are also given. We use this kinetic theory to discuss the processes of violent collisionless relaxation and slow collisional relaxation in systems with weak long-range interactions. In particular, we investigate the dependence of the relaxation time with the system size N and try to provide a coherent discussion of all the numerical results obtained for these systems.     

Long-time asymptotics of the long-range Emch-Radin model

The long-time asymptotic behaviour is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behaviour. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration.     

Upper Bound on the Decay of Correlations in a General Class of O(N)-Symmetric Models

We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, O(N)-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin correlations under all infinite-volume Gibbs measures. As a by-product, we also obtain estimates on the effective resistance of a (possibly long-range) resistor network in which randomly selected edges are shorted.     

Critical behavior at finite-temperature confinement transitions

Confinement in a pure gauge theory at non-zero temperature may be discussed in terms of an order parameter which transforms under a global symmetry group, the center of the gauge group. Integrating out all degrees of freedom except this order parameter generates an effective scalar field theory for the order parameter, globally invariant under the center symmetry. We argue that the effective theory possesses only short-range couplings, and hence that the finite-temperature confinement phase transition (when continuous) is accompanied by long-range fluctuations only in the order parameter. Universality ideas then lead to predictions for the critical properties of U(1), Z(N), and SU(N) gauge theories for all dimensionalities of space-time. An explicit renormalization-group calculation is presented for the U(1) gauge theory in (2 + 1) dimensions, the results of which fit the general picture.     

Renormalization character and quantum S-matrix for a classically integrable theory

The quantum theory of a N-component generalization of the sine-Gordon model is investigated. We find at the one-loop order that the model is renormalizable only when the corresponding classical theory is completely integrable: N = 1 (sine-Gordon model) and N = 2 (reduced O(4) σ-model). Moreover the coupling constant does nor renormalize in these two cases. Although the S-matrix for N = 2 is factorizable at the tree level, an anomaly appears at the one-loop order. Its effect is like a local quartic coupling.     

Liquid–gas and other unusual thermal phase transitions in some large-N magnets

Much insight into the low temperature properties of quantum magnets has been gained by generalizing them to symmetry groups of order N, and then studying the large-N limit. In this paper we consider an unusual aspect of their finite temperature behavior—their exhibiting a phase transition between a perfectly paramagnetic state and a paramagnetic state with a finite correlation length at N=∞. We analyze this phenomenon in some detail in the large “spin” (classical) limit of the SU(N) ferromagnet which is also a lattice discretization of the CP^N−1 model. We show that at N=∞ the order of the transition is governed by lattice connectivity. At finite values of N, the transition goes away in one or less dimension but survives on many lattices in two dimensions and higher, for sufficiently large N. The latter conclusion contradicts a recent conjecture of Sokal and Starinets [Nucl. Phys. B 601 (2001) 425], yet is consistent with the known finite temperature behavior of the SU(2) case. We also report closely related first order paramagnet–ferromagnet transitions at large N and shed light on a violation of Elitzur's theorem at infinite N via the large-q limit of the q state Potts model, reformulated as an Ising gauge theory.     

Effect of Oxygen Nonstoichiometry on the Magnetic Phase Transitions in Frustrated YBaCo<Subscript>4</Subscript>O<Subscript>7 + <Emphasis Type="Italic">x</Emphasis></Subscript> (<Emphasis Type="Italic">x</Emphasis> = 0, 0.1, 0.2) Cobaltites

The structural and elastic characteristics of YBaCo₄O_{7 + x} (x = 0, 0.1, 0.2) cobaltites synthesized by various technologies and having various excess oxygen contents x are experimentally studied. The distortion of the crystal structure in stoichiometric samples is found to remove frustrations and to bring about a longrange magnetic order in the cobalt subsystem, which is accompanied by well-pronounced anomalies in the elastic properties in the temperature range of a magnetic phase transition T_N. At a weak deviation from oxygen stoichiometry, the structure distortion disappears, frustrations are retained, and the further development of a long-range magnetic order is hindered. As a result of an absent long-range magnetic order, the anomalies of the elastic characteristics at T_N smooth rapidly and disappear. This finding points to the suppression of structural and magnetic transitions in nonstoichiometric samples and to the conservation of only short-range correlations of order parameter. It is found that nonstoichiometric samples can be separated into two phases depending on the ceramic synthesis conditions.     

Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets

We investigate the effect of geometry on the ground-state ordering of artificially frustrated magnetic rectangular and triangular lattices by Monte Carlo method. By varying the vertical lattice spacing while keeping the horizontal one fixed, we show that when the ratio of vertical to horizontal lattice spacing, labeled by η, is less than 1.82, the ground state of the rectangular lattice presents long-range antiferromagnetic order and for η?1.82 the ground state changes to long-range mixed ferromagnetic and antiferromagnetic order. For the frustrated triangular lattice, the short-range ordered state as well as two long-range ordered ground states occurs transiently at η=0.87 and 2, where the energies of the two ground states with long-range order are approximately equal. In addition, the level of frustration of both frustrated lattices is found to be largely relevant to the ratio η.     

Upper bound to the spin correlation function of the n-vector model with random anisotropic interactions

We obtain an upper bound to the spin correlation function in the thermodynamic limit of the zero external field limit for the n-vector model with random anisotropic interactions. We find a sufficient condition for disappearance of the spontaneous long-range order.     

Non-perturbative calculation of the mass-gap in the Gross-Neveu model

We calculate a fully renormalizable effective action for local composite operators in the U(N) Gross-Neveu model, recently introduced by one of us, to two loop order. We obtain results for the massgap in one and two loops which are optimized using the Grunberg method of effective charges. At one loop the accuracy is of the order of 2% or less (except for N = 2). At two loops the accuracy is significantly improved for N ≥ 5.     

Renormalization and phase transition in the quantum ofCPN−1 model (D=2,3)

We prove in the framework of the 1/N expansion the ultraviolet renormalizibility of the ofCP^N?1 model when D = 2, 3. It is shown that when D = 2 the model gains infrared divergences in higher orders of 1/N. When D = 3, the phase transition of second order occurs: above the critical points there exist N massive scalar charged particles and one particle corresponding to the massless isoscalar vector field, but below it there exist only N ? 1 massless particles.     

Quasi-periodic breathers in Hamiltonian networks of long-range coupling

This work is concerned with Hamiltonian networks of weakly and long-range coupled oscillators with either variable or constant on-site frequencies. We derive an infinite dimensional KAM-like theorem by which we establish that, given any N-sites of the lattice, there is a positive measure set of small amplitude, quasi-periodic breathers (solutions of the Hamiltonian network that are quasi-periodic in time and exponentially localized in space) having N-frequencies which are only slightly deformed from the on-site frequencies.     

Limits on possible long-range strong interactions

Limits on the strength of possible long-range (van der Waals) strong interaction forces having the form V ∝ r^?N for 2 ?N?7 are established from an analysis of exotic atom data.     

Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.