Uncovering the secrets of the 2d random-bond Blume-Capel model

TL;DR

This paper investigates how bond randomness influences the ground state, phase diagram, and critical behavior of the 2D ferromagnetic Blume-Capel model, revealing violations of universality and phase transition modifications.

Contribution

It introduces a combined computational approach to analyze ground states and finite-temperature behavior, highlighting the impact of disorder on phase transitions and universality.

Findings

Bond randomness enhances ferromagnetic order.

Strong violation of universality along the second-order transition line.

Ground states computed via maximum flow method.

Abstract

The effects of bond randomness on the ground-state structure, phase diagram and critical behavior of the square lattice ferromagnetic Blume-Capel (BC) model are discussed. The calculation of ground states at strong disorder and large values of the crystal field is carried out by mapping the system onto a network and we search for a minimum cut by a maximum flow method. In finite temperatures the system is studied by an efficient two-stage Wang-Landau (WL) method for several values of the crystal field, including both the first- and second-order phase transition regimes of the pure model. We attempt to explain the enhancement of ferromagnetic order and we discuss the critical behavior of the random-bond model. Our results provide evidence for a strong violation of universality along the second-order phase transition line of the random-bond version.