Universality aspects of the d=3 random-bond Blume-Capel model

TL;DR

This study investigates how bond randomness influences the universality classes of the 3d Blume-Capel model, revealing compatibility with the 3d random Ising model and identifying a new universality class for certain transitions.

Contribution

It provides the first comprehensive finite-size scaling analysis of the 3d random-bond Blume-Capel model, discovering a new universality class and confirming the universality of the 3d random Ising class under bond randomness.

Findings

Second-order transition under randomness aligns with 3d random Ising universality class.

Evidence of a new universality class for transitions from the first-order regime.

Strong violation of universality principle in certain ex-first-order transitions.

Abstract

The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that, the second-order transition emerging under bond randomness from the first-order regime of the pure model, belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site- and bond-dilution). The second, amounts to a strong violation of universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.