In this thesis, we examine various aspects of phase transitions and critical phenomena of pure and disordered magnetic systems using a variety of numerical approaches. In particular, we employ the Metropolis and Wolff algorithms in order to study the finite-size scaling of the interfacial adsorption of the two-dimensional Blume-Capel model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. What is more, we review the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime and the relevant self-averaging properties of the system. Following, we turn our focus on exact ground-state calculations with the use of graph cut methods for the investigation of the critical behaviour of the two-dimensional random-field Ising model. We illustrate the effectiveness of the Boykov-Kolmogorov algorithm and implement it for carrying out a thorough research on the breakup length scale problem of the square and triangular lattice models. We address questions such as which law governs the scaling of the breakup length of the random-field Ising model and whether this law depends on the definition used for the ratio of ferromagnetic ground states over the overall number of samples or on the lattice geometry. Finally, an alternative robust approach based on the second-moment correlation length 휉 of the model as obtained from a recently developed fluctuation-dissipation formalism is undertaken and provides a clear-cut resolution of the model’s scaling description.
|Date of Award||Dec 2021|
|Supervisor||Nikolaos Fytas (Supervisor) & Martin Weigel (Supervisor)|