Properties of the multicritical point of +/- J Ising spin glasses on the square lattice

Abstract

We use numerical transfer-matrix methods to investigate properties of the multicriticalpoint 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 non-linear zero-field uniform susceptibilities, on strip of widths $4 \leq L \leq 16$ sites, from which we estimate the conformal anomaly $c$, the decay-of-correlations exponent $η$, and the linear and non-linear susceptibility exponents $γ/ν$ and $γ^{nl}/ν$, with the help of finite-size scaling and conformal invariance concepts. Our results are: $c=0.46(1)$; $0.187 \lesssim η\lesssim 0.196$; $γ/ν=1.797(5)$; $γ^{nl}/ν=5.59(2)$. A direct evaluation of correlation functions on the strip geometry, and of the statistics of the zeroth moment of the associated probability distribution, gives $η=0.194(1)$, 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 $γ^{nl}/ν=2 γ/ν+d$ (with space dimensionality $d=2$) is obeyed to rather good accuracy, thus showing no evidence of multiscaling behavior of the susceptibilities.