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Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

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  • de Sousa, J.Ricardo
  • de Albuquerque, Douglas F.

Abstract

By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one (N′ = 1) and two (N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.

Suggested Citation

  • de Sousa, J.Ricardo & de Albuquerque, Douglas F., 1997. "Critical properties of the classical XY and classical Heisenberg models: A renormalization group study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(3), pages 419-428.
    • Handle: RePEc:eee:phsmap:v:236:y:1997:i:3:p:419-428
    DOI: 10.1016/S0378-4371(96)00276-2
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    1. Adler, Joan & Holm, Christian & Janke, Wolfhard, 1993. "High-temperature series analyses of the classical Heisenberg and XY models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 201(4), pages 581-592.
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    Cited by:

    1. Santos-Filho, A. & Albuquerque, D.F. de & Santos-Filho, J.B. & Batista, T.S. Araujo, 2016. "Phase diagram of the classical Heisenberg model in a trimodal random field distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 133-139.

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