Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions

TL;DR

This study uses entropic sampling to show that quenched bond randomness converts a weak first-order transition in a triangular Ising antiferromagnet into a second-order transition with a new universality class, characterized by specific critical exponents.

Contribution

It demonstrates the disorder-induced transition from first-order to second-order in a specific frustrated 2D Ising model and characterizes its critical behavior and universality class.

Findings

First-order transition becomes second-order with randomness.

Critical exponents indicate a new universality class.

Continuous transition exhibits negative specific heat exponent.

Abstract

Using a Wang-Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions. We consider the case $R=J_{nnn}/J_{nn}=1$, for which the pure model is known to have a columnar ground state where rows of nearest-neighbor spins up and down alternate and undergoes a weak first-order phase transition from the ordered to the paramagnetic state. With the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first-order phase transition to a second-order phase transition and using the Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging, under random bonds, continuous transition shows a strongly saturating specific heat behavior, corresponding to a negative exponent $\alpha$, and belongs to a new distinctive universality class with $\nu=1.135(11)$, $\gamma/\nu=1.744(9)$, and $\beta/\nu=0.124(8)$. Thus, our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional (2d) systems without and with quenched disorder.