Field-driven transition in an Ising magnet with mixed interactions

TL;DR

This study uses transfer-matrix methods and finite-size scaling to accurately map the phase diagram of a 2D Ising magnet with mixed interactions, revealing a non-reentrant critical line and confirming Ising-like thermal scaling.

Contribution

It provides the first detailed phase diagram for a 2D Ising model with mixed positive and negative couplings under an external field, challenging previous reentrant predictions.

Findings

Critical line starts horizontally at zero temperature.

Thermal scaling exponent close to Ising value y_T=1.

Reentrant behavior predicted earlier is not observed.

Abstract

Transfer-matrix methods are used, in conjunction with finite-size scaling and conformal invariance concepts, to generate an accurate phase diagram for a two-dimensional square-lattice Ising spin-1/2 magnet, with couplings which are positive along one coordinate axis, and negative along the other, in a uniform external field. Our results indicate that the critical line starts horizontally at the zero-temperature end of the phase boundary, at variance with the reentrant behavior predicted in some earlier studies. Estimates of the thermal scaling exponent are very close to the Ising value $y_T=1$ along the critical line, except near T=0 where strong crossover effects prevent a reliable analysis.