Non-Standard Finite-Size Scaling at First-Order Phase Transitions

Abstract

We note that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., 1/L^3 for an L x L x L lattice in 3D) is transmuted to 1/L^2 scaling if there is an exponential low-temperature phase degeneracy. The gonihedric Ising model which has a four-spin interaction, plaquette Hamiltonian provides an exemplar of just such a system. We use multicanonical simulations of this model to generate high-precision data which provides strong confirmation of the non-standard finite-size scaling law. The dual to the gonihedric model, which is an anisotropically coupled Ashkin-Teller model, has a similar degeneracy and also displays the non-standard scaling.

Minor change of title (canonical ->standard) to match the version accepted for publication, some further explanation on numerical subtleties added, wider applicability of effect discussed, typos (hopefully) fixed, references added

References in corpus (5)

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• Exact solutions to plaquette Ising models with free and periodic boundaries
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