Symmetry, complexity and multicritical point of the two-dimensional spin glass

TL;DR

This paper uses symmetry and duality principles to analyze two-dimensional spin glasses, proposing a conjecture for the multicritical point and revealing simplified behaviors under specific conditions.

Contribution

It introduces a novel symmetry-based approach to locate the multicritical point in 2D spin glasses and explores the system's simplified properties under certain matrix conditions.

Findings

Symmetry properties of replicated partition functions are identified.

A conjecture for the multicritical point location is proposed.

Reduced complexity conditions are suggested for the edge Boltzmann matrix.

Abstract

We analyze models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge Boltzmann factors. It is shown that the applications of homogeneous and Hadamard inverses to the edge Boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions, suggesting that the system has special simplicities under such conditions. Using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram.