Using the Random-Cluster Model for Ising Model Simulations
M. Delboo (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Joseph M. Thijssen – Mentor (TU Delft - QN/Thijssen Group)
Elena Pulvirenti – Mentor (TU Delft - Applied Probability)
T. Van der Sar – Graduation committee member (TU Delft - QN/vanderSarlab)
J.L.A. Dubbeldam – Graduation committee member (TU Delft - Mathematical Physics)
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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.