Universality and Dynamical Behaviour in Pure and Disordered Spin-1 Models

Abstract

he present thesis deals with the Monte Carlo study of models under dilution due to a singleion anisotropy, giving rise to a number of cross-over phenomena. The models considered arethe Blume-Capel and spin-1 Baxter-Wu in a crystal field, both possessing a rich phase transitionbehaviour. Specifically, they tend to exhibit first-order-like traits, especially with the increaseof the strength of the crystal field. Thus, as one approaches their multicritical point, the studybecomes more complicated and elaborate, with finite-size effect appearing, especially for theBaxter-Wu case due to the triplet interactions leading to strong first-order-like characteristics.This work focuses on a number of interconnected topics. For the spin-1 Baxter-Wu modelunder a crystal field, the aim is placed in elucidating the order of the transition and the universality class, a topic that is riddled by discrepancies in the literature. One would expect,from the renormalisation group theory and phenomenological arguments utilising the similarBlume-Capel model and dilute Potts models, that in the high-temperature regime the modelundergoes a continuous transition that falls into the universality class of the spin-1/2 BaxterWu model. In fact, this is exactly the result recovered by the current work. Additionally, thedevelopment of a possibly improved method to further study the aforementioned system isattempted. Specifically, a hybrid algorithm is utilised and its dynamical scaling is thoroughlystudied in the model’s continuous-transitions regime. Such an approach could help in locatingand studying its pentacritical point.Since the two-dimensional Blume-Capel model has been thoroughly studied, especially inits pure form, in the current work it is considered under quenched disorder. Specifically, uncorrelated randomness is applied to the crystal-field strength, in the form of a bimodal distribution. In addition, an external oscillating magnetic field drives the model out of equilibrium.Studying this system in its multi-droplet regime, period averaged observables are calculatedand their susceptibilities are shown to scale like their counterparts on the pure equilibriummodel.

Date of Award	May 2024
Original language	English
Awarding Institution	Coventry University
Supervisor	Nikos Fytas (Supervisor) & Martin Weigel (Supervisor)