Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

TL;DR

This paper proposes conjectures for the exact locations of the multicritical points in the phase diagram of the +/- J Ising model on triangular and hexagonal lattices, using a duality and replica method approach, aligning well with numerical estimates.

Contribution

It introduces a novel conjecture for the multicritical points on these lattices using a duality transformation combined with the replica method, providing precise estimates.

Findings

Conjectured p_c=0.8358058 for triangular lattice.

Conjectured p_c=0.9327041 for hexagonal lattice.

Results agree with recent numerical estimates.

Abstract

A conjecture is given for the exact location of the multicritical point in the phase diagram of the +/- J Ising model on the triangular lattice. The result p_c=0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in excellent agreement with a numerical study. The method is a variant of duality transformation to relate the triangular lattice directly with its dual triangular lattice without recourse to the hexagonal lattice, in conjunction with the replica method.