Scaling, clusters and geometry

Abstract

This thesis is focused on the study of phase transitions and universal critical phenomena of spin lattice models. New Monte Carlo algorithms were developed that enable the investigation of such models. A new level of accuracy is achieved in the determination of the universal parameters of the most common type of critical transition in nature, the Ising transition in three dimensions. The work took place at the Lorentz Institute for theoretical physics, under the guidance of Prof. Dr. H. W. J. Bl\"ote. The main results of this thesis are in the field of theoretical and computational physics.