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 $\eta$, and the linear and non-linear susceptibility exponents $\gamma/\nu$ and $\gamma^{nl}/\nu$, with the help of finite-size scaling and conformal invariance concepts. Our results are: $c=0.46(1)$; $0.187 \lesssim \eta \lesssim 0.196$; $\gamma/\nu=1.797(5)$; $\gamma^{nl}/\nu=5.59(2)$. A direct evaluation of correlation functions on the strip geometry, and of the statistics of the zeroth moment of the associated probability distribution, gives $\eta=0.194(1)$, 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 $\gamma^{nl}/\nu=2 \gamma/\nu+d$ (with space dimensionality $d=2$) is obeyed to rather good accuracy, thus showing no evidence of multiscaling behavior of the susceptibilities.