Dimensional crossover in the quasi-two-dimensional Ising-O(3) model

TL;DR

This study uses Monte Carlo simulations to explore phase transitions in a quasi-2D Ising-O(3) model, revealing an Ising ordered phase and a single first-order transition influenced by inter-layer coupling, with implications for ferropnictide experiments.

Contribution

It provides the first detailed Monte Carlo analysis of the Ising-O(3) model on quasi-2D lattices, elucidating the nature of phase transitions and crossover behaviors.

Findings

Identification of an Ising ordered phase with disordered O(3) spins in quasi-2D

Observation of a single first-order transition at large 3D coupling

Qualitative explanation of ferropnictide structural and magnetic transitions

Abstract

We present results of our Monte Carlo simulation of the Ising-O(3) model on the two-dimensional (2D) and quasi-2D lattices. This model is an effective classical model for the stacked square-lattice $J_1$-$J_2$ Heisenberg model where the nearest neighbor ($J_1$) and next-nearest neighbor ($J_2$) couplings are frustrated and we assume that $J_2$ is dominant. We find an Ising ordered phase where the O(3) spins remain disordered in a moderate quasi-2D region. There is a single first order transition for a sufficiently large 3D coupling. Our results can provide a qualitative explanation on the experiments on ferropnictides, namely observed sequence and orders of the structural and magnetic transitions, in terms of the ratio between the inter-layer and intra-layer coupling.