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

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.

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