Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

TL;DR

This study uses advanced Monte Carlo simulations to investigate how quenched disorder affects the phase transitions in the two-dimensional Blume-Capel model, confirming universality and exploring disorder-induced transition smoothing.

Contribution

It provides high-precision numerical evidence supporting strong universality with logarithmic corrections in the disordered Blume-Capel model and explores disorder effects on first-order transitions.

Findings

Supports strong universality with logarithmic corrections

Evidence of transition smoothing from first- to second-order due to disorder

Aligns with previous renormalization-group and numerical studies

Abstract

Using high-precision Monte-Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques we study the effect of quenched disorder in the crystal-field coupling of the Blume-Capel model on the square lattice. We mainly focus on the part of the phase diagram where the pure model undergoes a continuous transition, known to fall into the universality class of the pure Ising ferromagnet. A dedicated scaling analysis reveals concrete evidence in favor of the strong universality hypothesis with the presence of additional logarithmic corrections in the scaling of the specific heat. Our results are in agreement with an early real-space renormalization-group study of the model as well as a very recent numerical work where quenched randomness was introduced in the energy exchange coupling. Finally, by properly fine tuning the control parameters of the randomness distribution we also qualitatively investigate the part of the phase diagram where the pure model undergoes a first-order phase transition. For this region, preliminary evidence indicate a smoothening of the transition to second-order with the presence of strong scaling corrections.