Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture

TL;DR

This paper proposes a conjecture for the exact position of the multicritical point in finite-dimensional spin glass models, unifying various numerical results through a generalized duality and gauge symmetry approach.

Contribution

It introduces a new conjecture based on duality and gauge symmetry that predicts the multicritical point locations in diverse spin glass models and lattices.

Findings

Derived formulas for multicritical points in various models.

Unified understanding of numerical results across models.

Relation for dual lattice multicritical points.

Abstract

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems to derive formulas which make it possible to understand all the relevant available numerical results in a unified way. The method applies to non-self-dual lattices as well as to self dual cases, in the former case of which we derive a relation for a pair of values of multicritical points for mutually dual lattices. The examples include the +-J and Gaussian Ising spin glasses on the square, hexagonal and triangular lattices, the Potts and Z_q models with chiral randomness on these lattices, and the three-dimensional +-J Ising spin glass and the random plaquette gauge model.