Orientational glass: full replica symmetry breaking in generalized spin glass-like models without reflection symmetry

TL;DR

This paper develops a full replica symmetry breaking solution for a generalized spin glass model with broken reflection symmetry, providing insights into orientational glasses and challenging previous assumptions about such systems.

Contribution

It explicitly constructs a FRSB solution for models with broken reflection symmetry, countering the belief that no such solution exists in these systems.

Findings

Constructed a FRSB solution for non-symmetric operators U.

Demonstrated the existence of FRSB in systems without reflection symmetry.

Provided a counterexample to the conjecture of no FRSB solutions in such systems.

Abstract

We investigate near the point of glass transition the expansion of the free energy corresponding to the generalized Sherrington--Kirkpatrick model with arbitrary diagonal operators U standing instead of Ising spins. We focus on the case when U is an operator with broken reflection symmetry. Such a consideration is important for understanding the behavior of spin-glass-like phases in a number of real physical systems, mainly in orientational glasses in mixed molecular crystals which present just the case. We build explicitly a full replica symmetry breaking (FRSB) solution of the equations for the orientational glass order parameters when the non-symmetric part of U is small. This particular result presents a counterexample in the context of usually adopted conjecture of the absence of FRSB solution in systems with no reflection symmetry.