Phase diagram and critical behavior of the square-lattice Ising model with competing nearest- and next-nearest-neighbor interactions

TL;DR

This study uses GPU-accelerated Monte Carlo simulations to analyze the phase diagram and critical behavior of a square-lattice Ising model with competing interactions, revealing continuous transitions, reentrance, and bicritical points.

Contribution

It provides large-scale simulation data confirming reentrant behavior and bicritical points in the Ising model with competing interactions, supporting Suzuki's weak universality.

Findings

Continuous phase transitions from ordered to paramagnetic phases.

Reentrant behavior of the critical line.

Existence of a bicritical point at zero temperature.

Abstract

Using the parallel tempering algorithm and GPU accelerated techniques, we have performed large-scale Monte Carlo simulations of the Ising model on a square lattice with antiferromagnetic (repulsive) nearest-neighbor(NN) and next-nearest-neighbor(NNN) interactions of the same strength and subject to a uniform magnetic field. Both transitions from the (2x1) and row-shifted (2x2) ordered phases to the paramagnetic phase are continuous. From our data analysis, reentrance behavior of the (2x1) critical line and a bicritical point which separates the two ordered phases at T=0 are confirmed. Based on the critical exponents we obtained along the phase boundary, Suzuki's weak universality seems to hold.