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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)

Abstract

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.

Keywords

Ising Model Critical Exponent Universality Class Harper Model Antiferromagnetic Potts Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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