2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212060This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.99 pages, 15 figures, submitted to Reviews in Computational ChemistryStatistical MechanicsStrongly Correlated Electronstext