Phase transitions in the two-dimensional super-antiferromagnetic Ising model with next-nearest-neighbor interactions

TL;DR

This study maps the phase diagram of a 2D super-antiferromagnetic Ising model with next-nearest-neighbor interactions, revealing critical lines of second-order transitions and the effects of interaction ratios on phase stability.

Contribution

It provides the first detailed phase diagram of the 2D SAF Ising model with nnn interactions using Monte Carlo and Transfer Matrix methods.

Findings

Existence of a SAF phase limited by second-order transition lines.

No evidence of first-order or re-entrant transitions.

Critical ratio R_c = 1/2 determines SAF phase stability.

Abstract

We use Monte Carlo and Transfer Matrix methods in combination with extrapolation schemes to determine the phase diagram of the 2D super-antiferromagnetic (SAF) Ising model with next-nearest-neighbor (nnn) interactions in a magnetic field. The interactions between nearest-neighbor (nn) spins are ferromagnetic along x, and antiferromagnetic along y. We find that for sufficiently low temperatures and fields, there exists a region limited by a critical line of 2nd-order transitions separating a SAF phase from a magnetically induced paramagnetic phase. We did not find any region with either first-order transition or with re-entrant behavior. The nnn couplings produce either an expansion or a contraction of the SAF phase. Expansion occurs when the interactions are antiferromagnetic, and contraction when they are ferromagnetic. There is a critical ratio R_c = 1/2 between nnn- and nn-couplings, beyond which the SAF phase no longer exists.