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.
KeywordsIsing Model Critical Exponent Universality Class Harper Model Antiferromagnetic Potts Model
Unable to display preview. Download preview PDF.
- M.E. Fisher, in Proc. Int. School of Physics ‘Enrico Fermi’, edited by M.S. Green, (Academic Press, New York, 1971), Vol. 51, p. 1.Google Scholar
- M.N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J.L. Lebowitz, (Academic Press, New York, 1983), Vol. 8, p. 146.Google Scholar
- K. Binder, in Finite Size Scaling and Numerical Simulation, edited by V. Privman, (World Scientific, Singapore, 1990), p. 173.Google Scholar
- M. Kikuchi and Y. Okabe, J. Magn. Magn. Mat. 104–107, 209 (1992).Google Scholar
- M. Kikuchi and Y. Okabe, J. Phys. Soc. Jpn., to appear.Google Scholar
- H. Hiramato and M. Kohmoto, Int. J. Mod. Phys., to appear.Google Scholar
- Y. Hashimoto, K. Niizeki and Y. Okabe, J. Phys. A, to appear.Google Scholar