Using the Random-Cluster Model for Ising Model Simulations

Bachelor thesis (2022)

Authors

M. Delboo Electrical Engineering, Mathematics and Computer Science

Contributors

J.M. Thijssen QN/Thijssen Group - AS (mentor)
E. Pulvirenti Applied Probability - EEMCS (mentor)
T. van der Sar QN/vanderSarlab - AS (graduation committee member)
J.L.A. Dubbeldam Mathematical Physics - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2022 Maxime Delboo
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Published Date

21-12-2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This thesis contains a rigorous derivation of the path integral formulation of the Isingmodel with multiple original proofs. Besides that, thesis also contains various resultsof simulations of the 2D square lattice Ising Model with nearest-neighbour interactionsusing the Swendsen-Wang algorithm. Using finite size scaling to find critical exponentγ, we reported a value of γ = 1.748 ± 0.004. After calculating the relaxation times τ forvarious thermodynamic variables, we found the value for the dynamic critical exponentz to be in the range of z = 0.180 ± 0.004 and z = 0.282 ± 0.005.