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Clusters in the three-dimensional Ising model with a magnetic field

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  • Wang, Jian-Sheng

Abstract

We study the clusters generated in the Swendsen-Wang algorithm in a magnetic field. It is shown that the number of clusters is related to that of Coniglio and Klein by simple factors. With this definition of clusters, infinite size appears whenever the system has a nonzero magnetization. Scaling behavior of the number of clusters near the critical point is confirmed. The number of clusters away from the critical point for large cluster size s is consistent with ln n ≌ |h|s − Γ s2 3 on the low temperature side of the Coniglio-Klein cluster percolation transition line, and is consistent with ln n≌−(|h| + c)s on the high temperature side. We also argue that this transition line is given by h = ±h̃(T)×(T-Tc)1 near Tc.

Suggested Citation

  • Wang, Jian-Sheng, 1989. "Clusters in the three-dimensional Ising model with a magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 161(2), pages 249-268.
    • Handle: RePEc:eee:phsmap:v:161:y:1989:i:2:p:249-268
    DOI: 10.1016/0378-4371(89)90468-8
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    Cited by:

    1. Wang, Jian-Sheng, 2021. "Phonon soft modes and para- to ferro-electric phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).

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