Bachelor Thesis: Monte Carlo Algorithms for Frustrated Systems
Table of Contents
Overview #
Un algoritmo di Monte Carlo per la simulazione di un sistema frustrato (A Monte Carlo Algorithm for the Simulation of a Frustrated System) Universita degli Studi di Pisa, Dipartimento di Fisica “E. Fermi”, 2013. Advisor: Dott. Giancarlo Cella.
This thesis investigates the performance of cluster Monte Carlo algorithms, specifically the Swendsen-Wang algorithm, when applied to frustrated spin systems, where the usual efficiency gains from cluster updates can break down.
Key Topics #
- Swendsen-Wang algorithm: A cluster-based Monte Carlo method that dramatically reduces critical slowing down in unfrustrated spin systems by flipping entire clusters of correlated spins in a single update.
- Frustration and critical slowing down: In frustrated systems, where competing interactions prevent all bonds from being simultaneously satisfied, the cluster decomposition becomes less effective. The thesis analyzes how frustration reintroduces critical slowing down.
- 2D Ising model: Benchmark simulations on the standard 2D Ising model to validate the implementation and measure dynamical critical exponents.
- O(N) nonlinear sigma model: Extension of the Swendsen-Wang approach to continuous spin models with Symanzik-improved lattice actions, exploring generalized update rules.