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 at finite temperature and symmetry breaking

For an infinite system of nucleons interacting through a central spin-isospin schematic force we discuss how the Hartree-Fock theory at finite temperature T yields back, in the T=0 limit, the standard zero-temperature Feynman theory when there is no symmetry breaking. The attention is focused on the mechanism of cancellation of the higher order Hartree-Fock diagrams and on the dependence of this cancellation upon the range of the interaction. When a symmetry breaking takes place it turns out that more iterations are required to reach the self-consistent Hartree-Fock solution, because the cancellation of the Hartree-Fock diagrams of order higher than one no longer occurs. We explore in particular the case of an explicit symmetry breaking induced by a constant, uniform magnetic field B acting on a system of neutrons. Here we compare calculations performed using either the single-particle Matsubara propagator or the zero-temperature polarization propagator, discussing under which perturbative scheme they lead to identical results (if B is not too large). We finally address the issue of the spontaneous symmetry breaking for a system of neutrons using the technique of the anomalous propagator: in this framework we recover the Stoner equation and the critical values of the interaction corresponding to a transition to a ferromagnetic phase.     

Dynamical Symmetry Breaking for Weinberg-Salam Model and Restoration at Finite Temperature

In this paper, we utilize Nambu-Jona-Lasinio (NJL) mechanism to discuss the dynamical symmetry breaking for Weinberg-Salam model. In the NJL mechanism the symmetry breaking not only is determined by the potential ofscalar field V(φ) but also has important relation with condensate of the fermion pair (φφ). We find that the coefficient of quadric term of scalar field μ² ≥ 0 can still cause symmetry breaking by virtue of (φφ) ≠ 0, and the vacuum expected value of scalar field obeys (φ) = (φφ), i.e., the order parameter which causes phase transition is the condensate of fermion pair (φφ). We also discuss the restoration problem of SU(2) × U(1) gauge symmetry breaking by the NJL mechanism at high temperatures.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

Symmetry breaking and restoration in Lifshitz type theories

We consider the one-loop effective potential at zero and finite temperature in scalar field theories with anisotropic space-time scaling. For z=2, there is a symmetry breaking term induced at one loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature. For z=3, we considered at first the case with a positive mass term at tree level and found no symmetry breaking effects induced at one loop, and then we study the case with a negative mass term at tree level where we cannot conclude about symmetry restoration effects at high temperature because of the imaginary parts that appear in the effective potential for small values of the scalar field.     

The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non-degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.     

Absence of an equilibrium ferromagnetic spin-glass phase in three dimensions

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.     

Symmetry breaking in Heisenberg antiferromagnets

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies the existence of a symmetry breaking in the state obtained by applying an infinitesimal symmetry-breaking field. The theorem is most meaningful when applied to a class of quantum antiferromagnets where the existence of a long range order has been proved by the Dyson-Lieb-Simon method. We also present a related theorem for the ground states. It is an improvement of the theorem by Kaplan, Horsch and von der Linden. Our lower bounds on the spontaneous staggered magnetization in terms of the long range order parameter take into account the symmetry of the system properly, and are likely to be saturated in general models.     

Shape Transition and Triaxial Interaction Effect in the Structure of 152-166Dy Isotopes

The positive parity states in even-even ^152-166Dy are studied systematically in the framework of the interacting boson model (IBM). A cubic term, L=3, has been added to the Hamiltonian in order to produce the effect of triaxiality on the energy spectrum. The potential energy surfaces as a function of β and γ deformation parameters, for all isotopes have been produced. Energy levels and reduced electric quadrupole transition probabilities are calculated in framework of IBM with Cubic term (IBMC). All results are compared with available experimental data. It is found that these isotopes can be described by a schematic Hamiltonian in transition from U(5) (vibration) to SU(3) (rotation) dynamic symmetry.     

Stability of the critical behavior of weakly disordered systems with respect to the introduction of an interaction potential breaking replica symmetry

The critical behavior of weakly disordered systems with a p-component order parameter is described using field-theoretic methods. A renormalization-group analysis of the effective model replica Hamiltonian with an interaction potential breaking replica symmetry is performed directly for three-dimensional systems in the two-loop approximation. For the case of a one-step replica symmetry breaking, fixed points of renormalization group equations are found using the Padé-Borel summation technique. It is established that the critical behavior of weakly disordered systems is stable with respect to replica symmetry breaking and that the former scenario of the influence of structural defects on the critical behavior of these systems is realized.     

Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field

The stability of a spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field Γ. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues λ_± of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when Γ is increased. Therefore, this result suggests that the study of the replicon cannot be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the λ_± indicate instability problems for the SG solution close to all ranges of a first order boundary.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Phase transitions in a fluid surface model with a deficit angle term

Nambu-Goto model is investigated by using the canonical Monte Carlo simulation technique on dynamically triangulated surfaces of spherical topology. We find that the model has four distinct phases; crumpled, branched-polymer, linear, and tubular. The linear phase and the tubular phase appear to be separated by a first-order transition. It is also found that there is no long-range two-dimensional order in the model. In fact, no smooth surface can be seen in the whole region of the curvature modulus α, which is the coefficient of the deficit angle term in the Hamiltonian. The bending energy, which is not included in the Hamiltonian, remains large even at sufficiently large α in the tubular phase. On the other hand, the surface is spontaneously compactified into a one-dimensional smooth curve in the linear phase; one of the two degrees of freedom shrinks, and the other degree of freedom remains along the curve. Moreover, we find that the rotational symmetry of the model is spontaneously broken in the tubular phase just as in the same model on the fixed connectivity surfaces.     

Induced Chern-Simons term of a paired electron state in the quantum Hall system

The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the usual term proportional to a filling factor due to P (parity) & T (time reversal) symmetry breaking but also correction terms due to P & T & U(1) symmetry breaking. The correction term essentially comes from the Nambu-Goldstone mode and depends on an infrared limit. It is shown that the correction term is related to a topological number of a gap function in the momentum space.     

Monopoles in the presence of the Chern–Simons term via the Julia–Toulouse approach

We study QED₃ with magnetic-like defects using the Julia–Toulouse condensation mechanism (JTM) introduced in [F. Quevedo, C.A. Trugenberger, Nucl. Phys. B 501 (1997) 143, arXiv:hep-th/9604196]. By a careful treatment of the symmetries we suggest a geometrical interpretation for distinct debatable issues in the MCS-monopole system: (i) the induction of the non-conserved electric current together with the Chern–Simons term (CS), (ii) the deconfinement transition and, (iii) the computation of the fermionic determinant in the presence of Dirac string singularities. The JTM leads to proper interpretation of the non-conserved current as originating from Dirac brane symmetry breaking. The mechanism behind this symmetry breaking is clarified. The physical origin of the deconfinement transition becomes evident in the low energy effective theory induced by the JTM. The proper procedure to compute the fermionic determinant in the presence of Dirac branes will be presented. A byproduct of this approach is the possible appearance of statistical transmutation and the clarification for the different quantization rules for the topological mass.     

PT-symmetry breaking in resonant tunneling heterostructures

We present fermionic model based on symmetric resonant tunneling heterostructure, which demonstrates spontaneous symmetry breaking in respect to combined operations of space inversion (P) and time reversal (T). PT-symmetry breaking manifests itself in resonance coalescence (collapse of resonances). We show that resonant energies are determined by eigenvalues of auxiliary pseudo-Hermitian PT-invariant Hamiltonian.     

The spin and pseudospin symmetries in the relativistic formalism: Similarities and differences

The effects of the symmetry breaking terms, spin-orbit potential (SOP) and pseudospin-orbit potential (PSOP), in the spin and pseudospin symmetries, respectively, are studied in a comparative way. The analytical properties of the small component F of the Dirac spinor for pseudospin doublets (PSDs) are investigated around the singularity point of the PSOP. We show that the PSOP and the pseudocentrifugal barrier must be appropriately related to each other to describe adequately the wave functions in the nuclear surface, whereas it is not the case for the centrifugal barrier and the SOP. We also determine a modified PSOP smaller than the PSOP when the parameter ˉ, appearing in it, is left to vary in the domain of real numbers. The inclusion of this modified PSOP allows us to define a continuous way that connects the two states of a PSD as ˉ varies continuously between the physical (integer) values of ˉ corresponding to these states. Our results indicate that whereas the SOP can be considered as a small spin symmetry breaking term that allows a simple explanation of the spin symmetry, the consideration of the PSOP as the pseudospin symmetry breaking term presents serious difficulties. Thus, we propose a new strategy to explain, in a simple way, the quasi-degeneracy of the PSDs.     

电子关联作用对Jahn-Teller效应引起的结构相变的影响

本文从考虑集体Jahn-Teller效应和电子关联作用的哈密顿量出发,研究Jahn-Teller效应所致的结构相变行为随作用量中各参量的变化情况。根据这些参量的不同选择,得到三种结果:(1)体系仅存在对称破缺的一个相变点;(2)体系在高温时存在对称破缺的相变,在低温时对称性又回复;(3)不存在结构相变。 关键词：     

Symmetry Breaking Ground States of Bose-Einstein Condensates in 1D Double Square Well and Optical Lattice Well

We investigate the phenomena of symmetry breaking and phase transition in the ground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an optical lattice well, respectively. By using standing-wave expansion method, we present symmetric and asymmetric ground state solutions of nonlinear Schrödinger equation (NLSE) with a symmetric double square well potential for attractive nonlinearity. In particular, we study the ground state wave function's properties by changing the depth of potential and atomic interactions (here we restrict ourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal a phase transition of BECs trapped in one-dimensional optical lattice potential.     

Gauge invariance and spontaneous symmetry breaking in two-gap superconductors

The gauge symmetry of the Ginzburg–Landau theory for two-gap superconductors is analyzed in this letter. We argue that the existence of two different phases, associated with the two independent scalar Higgs fields, explicitly breaks the gauge symmetry of the Ginzburg–Landau Hamiltonian, unless a new additional vector field is included. Furthermore, the interference term, or Josephson coupling, holding a direct dependence with the phase difference, also explicitly breaks down the gauge symmetry. We show that a solution for the problem is achieved by adding an additional kinetic coupling term between the two vector fields, which generates the desired terms through a spontaneous symmetry breaking mechanism. Finally, the electrodynamics of the system is also presented in terms of the supercurrents inside the superconducting region.