Multicritical Points of Potts Spin Glasses on the Triangular Lattice

TL;DR

This paper predicts the locations of multiple multicritical points in Potts spin glass models on the triangular lattice, using a novel duality technique to verify the conjecture's accuracy across different models.

Contribution

It introduces the direct triangular duality method to identify multicritical points in Potts spin glasses, expanding the understanding of phase transitions in these systems.

Findings

Identified continuous multicritical lines for two-state Potts spin glasses.

Provided numerous examples validating the conjecture for spin glass models.

Achieved highly precise locations of multicritical points using the new technique.

Abstract

We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with two- and three-body interactions on the triangular lattice. These results provide us with numerous examples to further verify the validity of the conjecture, which has succeeded in deriving highly precise locations of multicritical points for several spin glass models. The technique, called the direct triangular duality, a variant of the ordinary duality transformation, directly relates the triangular lattice with its dual triangular lattice in conjunction with the replica method.