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

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.