2. An extended summary of results and bibliography can be found in the review article by Wu (1982) and references therein. The exact relation connecting the Jones polynomial to a Potts partition function is given below. In a Monte Carlo Potts model, a microstructure is discretized using a regular grid (Potts, 1952; Wu, 1982). Here, we review the cellular Potts model (CPM; also … Wu published yet another extremely well-received review on knot theory and its connection with lattice statistical The Potts model, proposed by Renfrey B. Potts in 1952 , is a generalisation of the Ising model to more than two components. For a general discussion on Potts models see Refs .In practice one has a lattice system. This model has been exactly solved by Baxter and Wu , for the spin-1/2 case, where σ i = ± 1, and it is known ever since as the Baxter–Wu (BW) model.The ground state is four-fold degenerated: one ferromagnetic phase with all spins in the + 1 state, and three ferrimagnetic phases where two spins in the elementary triangle are in the − 1 state and the other one in the + 1 state. It generalizes the Ising model so that each spin can have more than two values. The Potts model (Potts 1952) has received an increasing theoretical and experimental interest in recent years, and at present a great many rigorous and approximate results are known. 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. 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). At more than one hundred citations per year ever since it was published, it is one of the most cited papers in physics5. The computation of the partition function is a very hard problem. It is shown that the quantities of interest arising in the percolation problem, including the Wu’s 1982 review on the Potts model is another classic . Percolation and the Potts Model F. Y. Wu 1 Received July 13, 1977 The Kasteleyn-Fortuin formulation of bond percolation as a lattice statistical model is rederived using an alternate approach. It includes the ice-vertex and bond percolation models as special cases. However, V. F. R. Jones observed an amazing connection between this problem and knot theory. The Kasteleyn-Fortuin formulation of bond percolation as a lattice statistical model is rederived using an alternate approach. The Potts model is also related to the Jones polynomial in the knot theory via the thread of the Temperley-Lieb algebra [9, 19]. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. The model can be studied on The statistical mechanics model obtained by assuming that each individual can be in one of q (where q > 2) states in the Ising model. We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. Percolation and the Potts model Wu, F. Y. Abstract. The sites of the lattice can be occupied by particles of different species, .. Potts model see Wu, (4,5)) More recently, Essam and Tsalls(6) uncovered the connection of the Potts model with the flow polynomial in graph theory, (7,8) and this consideration has since been extended to multisite correlation functions(9) and their applications(1O) and the associated duality Mathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tissue morphogenesis.
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