Multicritical point of Ising spin glasses on triangular and honeycomb lattices

TL;DR

This study investigates the multicritical point of 2D Ising spin glasses on triangular and honeycomb lattices using transfer-matrix methods, finite-size scaling, and conformal invariance, providing precise estimates and insights into their critical behavior.

Contribution

The paper offers the first accurate estimates of the multicritical point and critical exponents for Ising spin glasses on these lattices, confirming a recent conjecture and analyzing conformal invariance adaptations.

Findings

Precise location of multicritical points on both lattices.

Critical exponents differ from percolation values.

Correlation functions obey conformal invariance with geometric adjustments.

Abstract

The behavior of two-dimensional Ising spin glasses at the multicritical point on triangular and honeycomb lattices is investigated, with the help of finite-size scaling and conformal-invariance concepts. We use transfer-matrix methods on long strips to calculate domain-wall energies, uniform susceptibilities, and spin-spin correlation functions. Accurate estimates are provided for the location of the multicritical point on both lattices, which lend strong support to a conjecture recently advanced by Takeda, Sasamoto, and Nishimori. Correlation functions are shown to obey rather strict conformal-invariance requirements, once suitable adaptations are made to account for geometric aspects of the transfer-matrix description of triangular and honeycomb lattices. The universality class of critical behavior upon crossing the ferro-paramagnetic phase boundary is probed, with the following estimates for the associated critical indices: $\nu=1.49(2)$, $\gamma=2.71(4)$, $\eta_1= 0.183(3)$, distinctly different from the percolation values.