Application of Finite-Size Scaling to Phase Transitions and Localization-Delocalization Transitions

  • Y. Okabe
  • M. Kikuchi
  • K. Niizeki
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 75)


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.


Ising Model Critical Exponent Universality Class Harper Model Antiferromagnetic Potts Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Y. Okabe
    • 1
  • M. Kikuchi
    • 2
  • K. Niizeki
    • 1
  1. 1.Department of PhysicsTohoku UniversitySendaiJapan
  2. 2.Department of PhysicsOsaka UniversityToyonakaJapan

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