Possibly Exact Solution for the Multicritical Point of Finite-Dimensional Spin Glasses

TL;DR

This paper proposes a conjecture for the exact position of the multicritical point in finite-dimensional spin glasses, unifying various numerical results and suggesting the absence of finite-temperature transitions in certain symmetric models.

Contribution

It introduces a conjecture that precisely locates the multicritical point in finite-dimensional spin glasses, connecting theory with numerical findings across multiple models.

Findings

Unified understanding of numerical results across models

Conjecture for the exact multicritical point location

Prediction of no finite-temperature transition in symmetric models

Abstract

After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimensional spin glasses. The theory enables us to understand in a unified way many numerical results for two-, three- and four-dimensional models including the +-J Ising model, random Potts model, random lattice gauge theory, and random Zq model. It is also suggested from the same theoretical framework that models with symmetric distribution of randomness in exchange interaction have no finite-temperature transition on the square lattice.