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Monte Carlo Simulations of Spin Systems

  • Wolfhard Janke

Abstract

This chapter gives a brief introduction to Monte Carlo simulations of classical O(n) spin systems such as the Ising (n = 1), XY (n = 2), and Heisenberg (n = 3) models. In the first part I discuss some aspects of the use of Monte Carlo algorithms to generate the raw data. Here special emphasis is placed on nonlocal cluster update algorithms which proved to be most efficient for this class of models. The second part is devoted to the data analysis at a continuous phase transition. For the example of the three-dimensional Heisenberg model it is shown how precise estimates of the transition temperature and the critical exponents can be extracted from the raw data. I conclude with a brief overview of recent results from similar high-precision studies of the Ising and XY models.

Keywords

Monte Carlo Correlation Length Ising Model Spin System Critical Exponent 
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 1996

Authors and Affiliations

  • Wolfhard Janke
    • 1
  1. 1.Institut für PhysikJohannes Gutenberg-UniversitätMainzGermany

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