On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses

TL;DR

This study investigates the multicritical point of 2D Ising spin glasses on various lattices with different disorder types, using transfer-matrix and finite-size scaling, confirming some conjectures and exploring universality of critical properties.

Contribution

It provides detailed numerical estimates of the multicritical point and critical exponents across different lattices and disorder types, testing conjectures and universality.

Findings

Agreement with conjectured multicritical point for square and triangular lattices with binary disorder.

Small discrepancies with conjectures for other lattice and disorder combinations.

Critical exponents are consistent across lattice types and disorder distributions, supporting universality.

Abstract

We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular and honeycomb lattices, with both binary and Gaussian disorder distributions. For square and triangular lattices with binary disorder, the estimated position of the multicritical point is in numerical agreement with recent conjectures regarding its exact location. For the remaining four cases, our results indicate disagreement with the respective versions of the conjecture, though by very small amounts, never exceeding 0.2%. Our results for: (i) the correlation-length exponent $\nu$ governing the ferro-paramagnetic transition; (ii) the critical domain-wall energy amplitude $\eta$; (iii) the conformal anomaly $c$; (iv) the finite-size susceptibility exponent $\gamma/\nu$; and (v) the set of multifractal exponents $\{\eta_k \}$ associated to the moments of the probability distribution of spin-spin correlation functions at the multicritical point, are consistent with universality as regards lattice structure and disorder distribution, and in good agreement with existing estimates.