Universality, frustration, and conformal invariance in two-dimensional random Ising magnets

We consider long, finite-width strips of Ising spins with randomly distribu ted couplings. Frustration is introduced by allowing both ferromagnetic and antiferromagnetic interactions. Free energy and spin-spin correlation func tions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponent s gamma/nu, alpha/nu, and /nu to be obtained, whenever a second-order trans ition is present. Low-temperature ordering persists for suitably small conc entrations of frustrated bonds, with a transition governed by pure-Ising ex ponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point alo ng either the temperature axis or the Nishimori line, one finds nondivergin g specific heats. A percolationlike ratio gamma/nu is found upon analysis o f the uniform susceptibility at the Nishimori point. Our data are also cons istent with frustration inducing a breakdown of the relationship between co rrelation-length amplitude and critical exponents, predicted by conformal i nvariance for pure systems. [S0163-1829(99)07533-5].