Analytical evidence for the absence of spin glass transition on self-dual lattices

TL;DR

This paper provides analytical evidence that there is no finite-temperature spin glass transition in certain self-dual lattice models, using duality relations and symmetry considerations to support the conclusion.

Contribution

It introduces a systematic duality-based method to determine the absence of a finite-temperature spin glass transition in self-dual lattice models, extending previous numerical results.

Findings

No finite-temperature spin glass transition on self-dual lattices for symmetric disorder distributions.

Duality relations help locate the multicritical point approximately, with potential for exact results.

Applicable to various models including Ising, Potts gauge glass, and higher-dimensional models.

Abstract

We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a precise but approximate location of the multicritical point on the Nishimori line. This method can be systematically improved to presumably give the exact result asymptotically. The duality analysis, in conjunction with the relationship between the multicritical point and the spin glass transition point for the symmetric distribution function of randomness, leads to the conclusion of the absence of a finite-temperature spin glass transition for the case of symmetric distribution. The result is applicable to the random bond Ising model with $\pm J$ or Gaussian distribution and the Potts gauge glass on the square, triangular and hexagonal lattices as well as the random three-body Ising model on the triangular and the Union-Jack lattices and the four dimensional random plaquette gauge model. This conclusion is exact provided that the replica method is valid and the asymptotic limit of the duality analysis yields the exact location of the multicritical point