On the existence of an intermediate phase in the antiferromagnetic Ising model on an face-centered cubic lattice

TL;DR

This paper uses Monte Carlo simulations to identify a third stable antiferromagnetic phase in the face-centered cubic Ising model, challenging previous assumptions and clarifying the sublattice structure for mean field analysis.

Contribution

It discovers an intermediate antiferromagnetic phase with specific symmetry and clarifies the correct sublattice structure, contradicting prior work.

Findings

Identification of a third stable AFM phase with I4_1/amd symmetry

Calculation of transition temperatures depending on second-neighbour interactions

Correction of the sublattice structure used in mean field theory

Abstract

We use Monte Carlo simulation to determine the stable structures in the second-neighbour Ising model on the face-centred cubic lattice. Those structures are L1_1 for strongly antiferromagnetic second neighbour interactions and L1_0 for ferromagnetic and weakly antiferromagnetic second neighbours. We find a third stable "intermediate" antiferromagnetic phase with I4_1/amd symmetry, and calculate the paramagnetic transition temperature for each. The transition temperature depends strongly on second neighbour interactions which are not frustrated. Our results contradict a recent paper, which also reported two different AFM structures and a new "intermediate" phase exists in this system. Here we show that the assumed sublattice structure in is inconsistent with the ground state. We determine a sublattice structure suitable for solving this problem with mean field theory.