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Critical temperature estimates for higher-spin Ising and Potts models.

James L Monroe1

  • 1Department of Physics, Penn State University, 100 University Drive, Beaver Campus, Monaca, Pennsylvania 15061, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
Summary

This study estimates critical temperatures for Ising and Potts models using a dynamical systems approach. The method provides accurate critical temperature estimates for various spin systems on square and cubic lattices, even where other methods fail.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Estimating critical temperatures for spin models is crucial for understanding phase transitions.
  • Existing methods for higher-spin Ising and Potts models have limitations, especially on specific lattice structures.

Purpose of the Study:

  • To present accurate critical temperature estimates for higher-spin Ising and Potts models.
  • To apply a novel Husimi tree, dynamical systems approach to lattice models.
  • To refine existing estimates and provide new ones where data is scarce.

Main Methods:

  • Utilizing a Husimi tree representation within a dynamical systems framework.
  • Applying the method to square and simple cubic lattices.
  • Comparing results with existing series expansion and exact solutions where available.

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Main Results:

  • Accurate critical temperature estimates were obtained for higher-spin Ising models on the square lattice, improving upon series expansion results.
  • Precise critical temperature estimates were derived for both Ising and Potts models on the simple cubic lattice.
  • The dynamical systems approach proved effective for spin values where other methods lacked accuracy or were unavailable.

Conclusions:

  • The Husimi tree, dynamical systems approach offers a computationally efficient and accurate method for determining critical temperatures.
  • This method provides valuable data for higher-spin models, particularly on the simple cubic lattice.
  • The approach is accessible, with all estimates obtainable on a personal computer.