Nonstandard Finite-Size Scaling at First-Order Phase Transitions

We note that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., 1/L³ for an L×L×L lattice in 3D) is transmuted to 1/L² 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 provide strong confirmation of the nonstandard 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 nonstandard scaling.