Spontaneous symmetry breaking in annealed and quenched gauge field models

The structure of annealed and quenched models with localU(1) gauge invariance is studied in terms of the Helmholtz free energy. The first non-trivial, or one-loop, account of fluctuations in the annealed model suggests that spontaneous symmetry breaking occurs in two and three dimensions, through a first-order phase transition. Within the same approximation scheme, the quenched model displays a continuous phase transition. A more complete account of the fluctuations in the annealed model changes the nature of the transition to a continuous one, whereas spontaneous symmetry breaking is then absent with quenched disorder.     

Phase diagram of randomly polymerized membrane

Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. Received: 3 December 1997 / Revised: 31 March 1998 / Accepted: 3 August 1998     

First-order phase transition and phase coexistence in a spin-glass model

We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with random magnetic interaction. The thermodynamics is worked out in the full replica symmetry breaking scheme. The model exhibits a high temperature/low density paramagnetic phase. As temperature decreases or density increases, a phase transition to a full replica symmetry breaking spin-glass phase occurs. The nature of the transition can be either of the second order or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter, a latent heat, and coexistence of phases.     

A model of intrinsic symmetry breaking

Different from the symmetry breaking associated with a phase transition, which occurs when the controlling parameter is manipulated across a critical point, the symmetry breaking presented in this Letter does not need parameter manipulation. Instead, the system itself suddenly undergoes symmetry breaking at a certain time during its evolution, which is intrinsic symmetry breaking. Through a polymer model, it is revealed that the origin of the intrinsic symmetry breaking is nonlinearity, which produces instability at the instance when the evolution crosses an inflexion point, where this instability breaks the original symmetry.     

Symmetry restoration in the asymmetric linear σ model at finite temperature

TheSU(2)xSU(2) asymmetric linear sigma model is studied in a mean field approximation. A first order transition persists up to a critical value of the symmetry breaking term where it terminates at a higher order point. For the physical value of the symmetry breaking we only see remmants of the phase transition.     

Mean-field theory for quenched reduced large-N gauge model

The reduced model à la Eguchi and Kawai, its quenched version and the Wilson theory in the string variable representation are studied by employing the loop expansion around the mean field. The spontaneous breakdown of the U(1)^d symmetry in the Eguchi-Kawai model is thoroughly investigated. It is shown that the quenched reduced model undergoes the first-order phase transition in excellent agreement with the Monte Carlo data. The quenched reduced model is shown to be equivalent to the standard Wilson theory by comparing with the string variable Wilson theory at any finite order in the loop expansion in the large-N limit.     

Entanglement, quantum phase transition and fixed-point bifurcation in the N-atom Jaynes-Cummings model with an additional symmetry breaking term

In the present work we analyze the quantum phase transition (QPT) in the N-atom Jaynes-Cummings model (NJCM) with an additional symmetry breaking interaction term in the Hamiltonian. We show that depending on the type of symmetry breaking term added the transition order can change or not and also the fixed point associated to the classical analogue of the Hamiltonian can bifurcate or not. We present two examples of symmetry broken Hamiltonians and discuss based on them, the interconnection between the transition order, appearance of bifurcation and the behavior of the entanglement.     

Infinite Range Interaction Model of a Structural Glass

In this paper a simple mean-field model for the liquid-glass phase transition is proposed. This is the low density D-dimensional system of N particles interacting via infinite-range oscillating potential. In the framework of the replica approach it is shown that such a system exhibits the phase transition between the high-temperature liquid phase and the low-temperature glass phase. This phase transition is described in terms of the standard one-step replica symmetry breaking scheme.     

Experimental evidence of a phase transition in a closed turbulent flow

We experimentally study the susceptibility to symmetry breaking of a closed turbulent von Kármán swirling flow from Re=150 to Re?10?. We report a divergence of this susceptibility at an intermediate Reynolds number Re=Re(χ)?90,000 which gives experimental evidence that such a highly space and time fluctuating system can undergo a "phase transition." This transition is furthermore associated with a peak in the amplitude of fluctuations of the instantaneous flow symmetry corresponding to intermittencies between spontaneously symmetry breaking metastable states.     

Abelian duality, confinement, and chiral-symmetry breaking in a SU(2) QCD-like theory

We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial S(1) x R(3). The absence of thermal fluctuations, and the fact that quantum fluctuations favor the vacuum with unbroken center symmetry in a weakly coupled regime, renders the interesting dynamics of these theories analytically calculable. Confinement and the generation of the mass gap in the gluonic sector are shown analytically. In this regime, theory exhibits confinement without continuous chiral-symmetry breaking. However, a flavor singlet chiral condensate (which breaks a discrete chiral symmetry) persists at arbitrarily small S(1). Under certain reasonable assumptions, we show that the theory exhibits a zero temperature chiral phase transition in the absence of any change in spatial center symmetry realizations.     

q-deformed phase space and its lattice structure

A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that lives on such a lattice are derived as wavefunctions in ordinaryx-space.     

q-deformed phase space and its lattice structure

A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that lives on such a lattice are derived as wavefunctions in ordinaryx-space.     

Freezing of Classical Fluids in a Quenched Random Potential

The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.     

Path integral approach to the full Dicke model

The full Dicke model describes a system of N identical two level-atoms coupled to a single mode quantized bosonic field. The model considers rotating and counter-rotating coupling terms between the atoms and the bosonic field, with coupling constants g₁ and g₂, for each one of the coupling terms, respectively. We study finite temperature properties of the model using the path integral approach and functional methods. In the thermodynamic limit, N→∞, the system exhibits phase transition from normal to superradiant phase, at some critical values of temperature and coupling constants. We distinguish between three particular cases, the first one corresponds to the case of rotating wave approximation, where g₁≠0 and g₂=0, the second one corresponds to the case of g₁=0 and g₂≠0, in these two cases the model has a continuous symmetry. The last one, corresponds to the case of g₁≠0 and g₂≠0, where the model has a discrete symmetry. The phase transition in each case is related to the spontaneous breaking of its respective symmetry. For each one of these three particular cases, we find the asymptotic behaviour of the partition function in the thermodynamic limit, and the collective spectrum of the system in the normal and the superradiant phase. For the case of rotating wave approximation, and also the case of g₁=0 and g₂≠0, in the superradiant phase, the collective spectrum has a zero energy value, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the model. Our analysis and results are valid in the limit of zero temperature, β→∞, in which, the model exhibits a quantum phase transition.     

Analytical treatment of fluctuation spectra at the symmetry breaking chaos transition

The phase transition of characteristic exponents describing the fluctuations of temporal coarse grained quantities is investigated for the symmetry breaking bifurcation. The discussion of the eigenvalues of the transfer operator clarifies the origin of the phase transition and leads to scaling relations in the vicinity of the bifurcation point.     

Statistical properties of many-particle spectra. IV. New ensembles by Stieltjes transform methods

New Gaussian matrix ensembles, with arbitrary centroids and variances for the matrix elements, are defined as modifications of the three standard ones—GOE, GUE and GSE. The average density and two-point correlation function are given in the general case in terms of the corresponding Stieltjes transforms, first used by Pastur for the density. It is shown for the centroid-modified ensemble K + αH that when the operator K preserves the underlying symmetries of the standard ensemble H, then, as the magnitude of α grows, the transition of the fluctuations to those of H is very rapid and discontinuous in the limit of asymptotic dimensionality. Corresponding results are found for other ensembles. A similar Dyson result for the effects of the breaking of a model symmetry on the fluctuations is generalized to any model symmetry, as well as to the fundamental symmetries such as time-reversal invariance.     

On spin systems with quenched randomness: Classical and quantum

The rounding of first-order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a d-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when d≤2. This implies absence of jumps in the associated order parameter, e.g., the magnetization in the case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for d≤4. Some questions concerning the behavior of related order parameters in such random systems are discussed.     

The flattening of the average potential in models with fermions

The average potential is a scale dependent scalar effective potential. In a phase with spontaneous symmetry breaking its inner region becomes flat as the averaging extends over infinite volume and the average potential approaches the convex effective potential. Fermion fluctuations affect the shape of the average potential in this region and its flattening with decreasing physical scale. They have to be taken into account to find the true minimum of the scalar potential which determines the scale of spontaneous symmetry breaking.     

Phase transition in the scalar noise model of collective motion in three dimensions

We consider disorder-order phase transitions in the three-dimensional version of the scalar noise model (SNM) of flocking. Our results are analogous to those found for the two-dimensional case [CITE]. For small velocity (v≤0.1) a continuous, second-order phase transition is observable, with the diffusion of nearby particles being isotropic. By increasing the particle velocities the phase transition changes to first order, and the diffusion becomes anisotropic. The first-order transition in the latter case is probably caused by the interplay between anisotropic diffusion and periodic boundary conditions, leading to a boundary condition dependent symmetry breaking of the solutions.