Universality from disorder in the random-bond Blume-Capel model

TL;DR

This study uses Monte Carlo simulations to show that quenched disorder in the random-bond Blume-Capel model softens first-order transitions into continuous ones, revealing a universality class similar to the disordered Ising model with logarithmic corrections.

Contribution

It demonstrates how quenched disorder transforms first-order transitions into continuous ones and identifies the universality class with logarithmic corrections in the disordered Blume-Capel model.

Findings

First-order transition becomes continuous with disorder.

Disordered system belongs to the Ising universality class with logarithmic corrections.

Finite-size effects show a crossover length scale around 32.

Abstract

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior in the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale $L^{\ast} \approx 32$ for the chosen parameters.