Application of Finite-Size Scaling to Phase Transitions and Localization-Delocalization Transitions
The computational studies of phase transitions using the finite-size scaling analysis are reported. First, we investigate the three-state Potts model by use of a Monte Carlo simulation. The finite-size scaling and the Monte Carlo renormalization group method are used to study the critical properties of the antiferromagnetic Potts model. The system of a random mixture of the ferromagnetic and antiferromagnetic couplings is also discussed. Next, the Ising model on the three-dimensional icosahedral quasilattice is studied. Investigating the critical phenomena on the basis of finite-size scaling, we confirm that the critical exponents are universal among regular lattices and quasilattices. Lastly, we show that the finite-size scaling analysis is also effective in analyzing the critical properties of the localization-derealization transition of the wave functions in quasi-periodic systems.
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