Transmuted finite-size scaling at first-order phase transitions

TL;DR

This paper investigates how exponential degeneracies in low-temperature phases alter finite-size scaling at first-order phase transitions, confirmed through simulations of a 3D gonihedric Ising model and related systems.

Contribution

It introduces a modified finite-size scaling law accounting for exponential degeneracies and validates it with high-precision simulations.

Findings

Modified 1/L^2 correction observed in the gonihedric Ising model

Exponential degeneracy leads to altered finite-size scaling behavior

Potential applicability to other models with degenerate low-temperature states

Abstract

It is known that fixed boundary conditions modify the leading finite-size corrections for an L^3 lattice in 3d at a first-order phase transition from 1/L^3 to 1/L. We note that an exponential low-temperature phase degeneracy of the form 2^3L will lead to a different leading correction of order 1/L^2 . A 3d gonihedric Ising model with a four-spin interaction, plaquette Hamiltonian displays such a degeneracy and we confirm the modified scaling behaviour using high-precision multicanonical simulations. We remark that other models such as the Ising antiferromagnet on the FCC lattice, in which the number of "true" low-temperature phases is not macroscopically large but which possess an exponentially degenerate number of low lying states may display an effective version of the modified scaling law for the range of lattice sizes accessible in simulations.