Iblisdir, SofyanJuliá-Díaz, BrunoGonchenko, MarinaDíaz Rodríguez, Juan Carlos2024-12-032024-12-032024-06-28https://hdl.handle.net/2445/216887Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Sofyan Iblisdir, Bruno Juliá-Díaz i Marina Gonchenko[en] We present a Metropolis-Hastings Markov chain for correlated systems of continuous variables ruled by the Boltzmann distribution. An initial introduction to the algorithm with discrete variables is given and then extended to variables in a compact group. We initially work with the SU (2) Higgs model with frozen matter term on a 2D lattice. The algorithm is then extended to a 3D lattice. The configuration updates are done though tensor network renormalization schemes that approximate the partition function of the system. We evaluate the performance of the chains based on equilibration and autocorrelation times. The mean value of different observables are compared to existing literature and additional computations are done with the groups SU (3), SU (5) and SU (10).57 p.application/pdfengcc by-nc-nd (c) Juan Carlos Díaz Rodríguez, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/Processos de MarkovMètode de MontecarloTreballs de fi de màsterTeoria dels reticlesMarkov processesMonte Carlo methodMaster's thesisLattice theoryinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess