Annealed Character of Spin Clusters in Ising Spin Systems

• Published in: Progress of theoretical and experimental physics 1997-07, Vol.98 (1), p.39-55
• Main Authors: Kasai, Yasuhiro, Imaoka, Hitoshi, Ohnaka, Kohzaburo
• Format: Article
• Language: English
• ISSN: 0033-068X; 2050-3911; 1347-4081
• DOI: 10.1143/PTP.98.39

An arbitrary Ising spin system can be expressed by a bond percolation system of spin clusters through the Kasteleyn-Fortuin transformation. The generating function of the percolation system with temperature and internal-freedom related variables can be expressed as the Legendre transformation of the entropy, where conjugate topological variables are the numbers of bonds and clusters in the respective cases. The percolation system has an annealed character whose bond configuration changes in the thermodynamic process. Even for a 2D strongly frustrated Ising system, at a finite temperature there exists a percolation transition which is a real singular point of the entropy. The annealed character determines the universality class as that of the ferromagnetic Potts model with one degree of internal freedom (random percolation). The reduced freedom hides the strong order in the generating function.