Properties of the multicritical point of±JIsing spin glasses on the square lattice

Abstract

We use numerical transfer-matrix methods to investigate properties of the multicritical point of binary Ising spin glasses on a square lattice, whose location we assume to be given exactly by a conjecture advanced by Nishimori and Nemoto. We calculate the two largest Lyapunov exponents, as well as linear and nonlinear zero-field uniform susceptibilities, on strip of widths 4 ഛ L ഛ 16 sites, from which we estimate the conformal anomaly c, the decay-of-correlations exponent , and the linear and nonlinear susceptibility exponents ␥ / and ␥ nl / , with the help of finite-size scaling and conformal invariance concepts. Our results are c = 0.46͑1͒; 0.187Շ Շ 0.196; ␥ / = 1.797͑5͒; ␥ nl / = 5.59͑2͒. A direct evaluation of correlation functions on the strip geometry, and of the statistics of the zeroth moment of the associated probability distribution, gives = 0.194͑1͒, consistent with the calculation via Lyapunov exponents. Overall, these values tend to be inconsistent with the universality class of percolation, though by small amounts. The scaling relation ␥ nl / =2␥ / + d ͑with space dimensionality d =2͒ is obeyed to rather good accuracy, thus showing no evidence of multiscaling behavior of the susceptibilities.