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It also shows that the 4-state Potts behavior without logarithmic factors can only occur at special points in the parameter space, where the two leading temperature ﬁelds simultaneously vanish. The Potts model is extended to include the case of block type many-body interaction. Abstract. If q = 2, the Potts model is reduced to the Ising model. The average spin spin correlation function, 6~,,~ j at the paramagnetic phase is t … )~Og(q-l) [J1 + (M - 1)h] . 14 The Potts model is also related to, and generalized by, several other models, such as the XY model, 15 the Heisenberg model 16 and the N-vector model. The Potts model FY Wu –Reviews of modern physics, 1982 Cited by 2964 figure from: Eyal Lubetzky, Courant Institute =3 =4 =5 The Kasteleyn-Fortuin formulation of bond percolation as a lattice statistical model is rederived using an alternate approach. Potts model based on a Markov process computation solves the community structure problem effectively HJ Li, Y Wang, LY Wu, J Zhang, XS Zhang Physical Review E 86 (1), 016109 , 2012 î‡˙(Soyzi, 1972) I q 3ž ,ˆØJ> 0‰J< Ñ÷v-c ^. 17 Generalizations of the Potts model have been used to model grain growth in metals and coarsening in foams. The exactly solved Baxter-Wu model [3] precisely ﬁts such a location in parameter space: it belongs to the 4-state Potts class and its If two neighboring spins i and j are in the same orientation, then they contribute an amount $-J$ to the total energy of a configuration. Percolation and the Potts model Wu, F. Y. Abstract. Essentially all the simulations based on the Monte Carlo Potts model were performed to study grain growth (Anderson et al., 1984; Wejchert et al., 1986). From standard mean field theory for the Potts model (Wu, 1982) it is possible to show that the transition from the ferromagnetic phase to the paramagnetic phase is at Tc = 2M (qJ. The first of these is the Q-state Potts model (Potts, 1952; Wu, 1982). The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. ⁄ › ÑJ>0ÚJ<0ü⁄…C: In a Monte Carlo Potts model, a microstructure is discretized using a regular grid (Potts, 1952; Wu, 1982). One assumes that each spin i can be in one of Q possible discrete orientations $\chi_i$ $(\chi_i =,1,2,\ldots,Q)$. We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. Each grid point is labeled by an integer number representing the orientation of a grain. It is shown that the quantities of interest arising in the percolation problem, including the critical exponents, can be obtained from the solution of the Potts model.