Absence of Replica Symmetry Breaking in the Random Field Mixed-Spin Ginzburg-Landau Model

TL;DR

This paper extends the random field Ginzburg-Landau model by incorporating p-spin interactions and demonstrates that, in the infinite volume limit, the variance of spin overlap diminishes, indicating no replica symmetry breaking occurs.

Contribution

It introduces the random field mixed-spin Ginzburg-Landau model and proves the absence of replica symmetry breaking in the infinite volume limit.

Findings

Variance of spin overlap vanishes in the infinite volume limit

No replica symmetry breaking occurs in the extended model

Generalizes previous models with added p-spin interactions

Abstract

In this paper, an extension of the random field Ginzburg-Landau model on the hypercubic lattice is considered by adding $p$-spin ($p\geqslant 2$) interactions coupled to general disorders. This new model is called the random field mixed-spin Ginzburg-Landau model. We proved that, in the infinite volume limit of this model, the variance of spin overlap vanishes.