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Generalization of the invaded cluster algorithm to the tricritical point

The invaded cluster algorithm [1] is generalized [2] to the tricritical point on the example of 2d Potts model with annealed dilution. Self-regulating procedure that locates the tricritical point in the two-parameter space spanned by temperature and chemical potential of vacancies is constructed based on geometrical arguments. The tricritical point is identified as a simultaneous percolation of the Fortuin-Kastelyn cluster and the geometrical cluster consisting of vacancies and isolated spins. The tricritical values of parameters and concentration are presented for q=1, 2, 3 and found to be in a good agreement with the best known results [3]. Scaling properties of the percolating scaling cluster and related critical exponents are also derived. Based on the idea that effective correlation of vacancies is important at the tricritical point, we also examine alternative stopping rules within generalized IC algorithm, and possible extension to higher dimensions. [1] J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. V. Chayes, Phys. Rev. Lett. 75, 2792 (1995) ; J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. M. Chayes, Phys. Rev. E 54, 1332 (1996). [2] I. Balog, K.Uzelac, preprint cond-mat/0703759. [3] X. Qian, Y. Deng, H. W. J. Bl¨ote, Phys. Rev. E 72, 056132 (2005).

Cluster algorithm; Monte Carlo simulations; Potts model; tricritical point

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