Finite-size scaling of Monte Carlo simulations for the fcc Ising antiferromagnet: Effects of the low-temperature phase degeneracy

TL;DR

This study investigates the finite-size scaling behavior of the fcc Ising antiferromagnet with high ground-state degeneracy, confirming a transmuted scaling form and estimating the transition temperature through Monte Carlo simulations.

Contribution

It demonstrates that the finite-size scaling of the fcc Ising antiferromagnet aligns with a transmuted scaling form due to low-temperature phase degeneracy, supported by extensive Monte Carlo data.

Findings

Transmuted finite-size scaling fits simulation data better than standard scaling.

Estimated transition temperature T0 = 1.735047(46).

Confirmed the influence of phase degeneracy on finite-size scaling behavior.

Abstract

The Ising antiferromagnet on a face-centered cubic (fcc) lattice with nearest-neighbor interaction only is well known to exhibit a macroscopic (exponential in the system size $L$) ground-state degeneracy. With increasing temperature, this degeneracy is expected to be lifted and the model undergoes a first-order phase transition. For a model with an exponential degeneracy in the whole low-temperature phase, it was recently found that the finite-size scaling behavior is governed by leading correction terms $\sim L^{-2}$ instead of $\sim L^{-3}$ as usual. To test the conjecture that such a transmuted behavior may effectively persist also for the fcc antiferromagnet up to some crossover system size, we have performed parallel multicanonical Monte Carlo simulations for lattices of linear size $L \le 18$ with periodic boundary conditions and determined various inverse pseudo phase transition temperatures, as well as the extremal values of the specific heat and the energetic Binder parameter. We indeed find that, for the simulated lattice sizes, the conjectured transmuted finite-size scaling ansatz fits the data better than the standard ansatz. On this basis, we extrapolate for the transition temperature an estimate of $T_0 = 1.735047(46)$.