Scaling behavior of a square-lattice Ising model with competing interactions in a uniform field

TL;DR

This study uses transfer-matrix methods and finite-size scaling to analyze the critical behavior of a 2D square-lattice Ising model with competing interactions and an external field, revealing continuously-varying exponents and deviations from classic Ising values.

Contribution

It provides new insights into the critical behavior and universality class of the Ising model with competing interactions under an external field, using advanced computational techniques.

Findings

Conformal anomaly c close to 1 along the critical curve.

Evidence of continuously-varying critical exponents.

Deviations from Ising-like critical exponents observed.

Abstract

Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor interactions, both antiferromagnetic, in a uniform external field. On the critical curve separating collinearly-ordered and paramagnetic phases, our estimates of the conformal anomaly $c$ are very close to unity, indicating the presence of continuously-varying exponents. This is confirmed by direct calculations, which also lend support to a weak-universality picture; however, small but consistent deviations from the Ising-like values $\eta=1/4$, $\gamma/\nu=7/4$, $\beta/\nu=1/8$ are found. For higher fields, on the line separating row-shifted $(2 \times 2)$ and disordered phases, we find values of the exponent $\eta$ very close to zero.