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

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

1999-06-08

arxiv.org/abs/cond-mat/9906114v1

Physical Review B 60, 6740 (1999)

Physics

Condensed Matter

Statistical Mechanics

RevTeX code for 10 pages, 9 eps figures, to appear in Physical Review B (September 1999)

Scientific paper

10.1103/PhysRevB.60.6740

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferro- and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $\gamma/\nu$, $\alpha/\nu$ and $\nu$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure--Ising exponents. 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 along either the temperature axis or the Nishimori line, one finds non-diverging specific heats. A percolation-like ratio $\gamma/\nu$ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems.

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