Absence Of Replica Symmetry Breaking Research Articles

Absence of replica symmetry breaking in disordered FKG-Ising models under uniform field

We prove that the variance of a spin overlap vanishes in disordered Ising models satisfying the Fortuin–Kasteleyn–Ginibre inequality under a uniform field, such as the generally distributed random field Ising model and site- and bond-diluted Ising models with the Bernoulli distribution. Chatterjee’s proof for the Gaussian random field Ising model is generalized to another independent identically distributed quenched disorder under a uniform field.

Issues of replica-symmetry breaking for the amorphous solid state of vulcanized macromolecules

The statistical mechanics of vulcanized (i.e. permanently randomly crosslinked) macromolecular matter can be formulated, using the replica technique, as the n to 0 limit of a theory containing n+1 coupled replicas. Within the framework of a replica-symmetric variational mean-field approach, this theory describes an equilibrium phase transition, upon sufficient vulcanization, from a liquid to an amorphous solid state. We consider a natural extension of this framework, which admits the possibility of the spontaneous breaking of replica symmetry, and find that-at least at the mean-field level-replica symmetry appears to remain intact. We discuss the physical origin of this absence of replica-symmetry breaking, as well as a possible strategy for a theoretical refinement that may yield replica-symmetry breaking.

Sherrington-Kirkpatrick model in a transverse field: Absence of replica symmetry breaking due to quantum fluctuations.

The Sherrington-Kirkpatrick model under a transverse field is studied here employing the Suzuki-Trotter formula to map the model to an equivalent classical one. The effective Thouless-Anderson-Palmer free energy is used to study the stability of the system, and Monte Carlo computer simulations of the effective classical model are performed to obtain the phase diagram and the magnetization overlap distribution. Our results indicate a trivial overlap distribution due to quantum fluctuations. The phase diagram shows a slight initial increase in the glass transition temperature ${T}_{g}$ as the transverse field is switched on, confirming that obtained by Yokota.

Nonlinear relaxation and ergodicity breakdown in random anisotropy spin glasses

An exact theory of the nonlinear relaxation of a zero-dimensional magnetic anisotropy model is derived in the large- n limit where n is the number of the spin components. We consider both the “pure” and “random” case. In the random case the magnetization decays asymptotically with an inverse time power. This result is shown to be in agreement with the numerical solution of the model in the case of a large but finite n. We find a new ergodicity breaking phenomenon associated with the nonlinear relaxation in the spin glass which occurs even in the absence of replica symmetry breaking in the steady state.