Field-induced Ordering in Critical Antiferromagnets

TL;DR

This study uses transfer-matrix scaling to analyze critical properties of field-induced phase transitions in two 2D antiferromagnets, revealing how critical lines and correlation lengths behave near zero temperature and field.

Contribution

It provides new estimates of critical line slopes and divergence of correlation lengths for triangular-lattice Ising and three-state Potts models under magnetic fields.

Findings

Critical line leaves zero-temperature fixed point at finite angle for TIAF.

Correlation length diverges exponentially as temperature approaches zero for SPAF-3.

Conformal anomaly and decay exponents change with applied field in SPAF-3.

Abstract

Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antiferromagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Our main findings are summarised as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero -field fixed point at a finite angle. Our best estimate of the slope at the origin is $(dT_c/dH)_{T=H=0} = 4.74 \pm 0.15$. For SPAF-3 we provided evidence that the zero-field correlation length diverges as $\xi(T \to 0, H=0) \simeq \exp (a/T^{x})$, with $x=1.08 \pm 0.13$, through analysis of the critical curve at $H \neq 0$ plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as: (a) H=0: $c=1, \eta=1/3$; (b) $H \neq 0: c=1/2, \eta=1/4$.