Se p 20 01 Transfer Matrices and Partition - Function Zeros for Antiferromagnetic Potts Models
نویسندگان
چکیده
We study the chromatic polynomials for m × n square-lattice strips, of width 9 ≤ m ≤ 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n → ∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.
منابع مشابه
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models IV. Chromatic polynomial with cyclic boundary conditions
We study the chromatic polynomial PG(q) for m× n squareand triangular-lattice strips of widths 2 ≤ m ≤ 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin–Kasteleyn representation for such lattices and obtai...
متن کاملA pr 2 00 2 Transfer Matrices and Partition - Function Zeros for Antiferromagnetic Potts Models III . Triangular - lattice chromatic polynomial
We study the chromatic polynomial PG(q) for m×n triangular-lattice strips of widths m ≤ 12P, 9F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such...
متن کاملA pr 2 00 3 Transfer Matrices and Partition - Function Zeros for Antiferromagnetic Potts Models III . Triangular - lattice chromatic polynomial
We study the chromatic polynomial PG(q) for m×n triangular-lattice strips of widths m ≤ 12P, 9F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such...
متن کامل0 Transfer Matrices and Partition - Function Zeros for Antiferromagnetic Potts Models II . Extended results for square - lattice chromatic polynomial
We study the chromatic polynomials for m × n square-lattice strips, of width 9 ≤ m ≤ 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n → ∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some...
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The q-state Potts model can be defined on an arbitrary finite graph, and its partition function encodes much important information about that graph, including its chromatic polynomial, flow polynomial and reliability polynomial. The complex zeros of the Potts partition function are of interest both to statistical mechanicians and to combinatorists. I give a pedagogical introduction to all these...
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