Partial annealing of a coupled mean-field spin-glass model with an embedded pattern

TL;DR

This paper investigates a partially annealed mean-field spin-glass model with an embedded pattern, revealing phase transitions and the influence of temperature ratios on pattern stability and system behavior.

Contribution

It introduces a new model with partial annealing, showing how interaction correlations and phase diagrams depend on temperature ratios, and identifies reentrant transitions unique to this setup.

Findings

Three distinct phases: paramagnetic, ferromagnetic, spin-glass.

Reentrant transition from ferromagnetic to spin-glass phase.

Embedded pattern stability depends on temperature ratio n.

Abstract

A partially annealed mean-field spin-glass model with a locally embedded pattern is studied. The model consists of two dynamical variables, spins and interactions, that are in contact with thermal baths at temperatures T_S and T_J, respectively. Unlike the quenched system, characteristic correlations among the interactions are induced by the partial annealing. The model exhibits three phases, which are paramagnetic, ferromagnetic and spin-glass phases. In the ferromagnetic phase, the embedded pattern is stably realized. The phase diagram depends significantly on the ratio of two temperatures n=T_J/T_S. In particular, a reentrant transition from the embedded ferromagnetic to the spin-glass phases with T_S decreasing is found only below at a certain value of n. This indicates that above the critical value n_c the embedded pattern is supported by local field from a non-embedded region. Some equilibrium properties of the interactions in the partial annealing are also discussed in terms of frustration.