相关论文: Transfer Matrices for the Partition Function of th…
We present a method for calculating transfer matrices for the $q$-state Potts model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature variable $v$, on cyclic and M\"obius strip graphs $G$ of the square (sq), triangular…
We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and…
partial abstract: The $q$-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form…
We present exact calculations of the partition function for the q-state Potts model for general q, temperature and magnetic field on strips of the square lattices of width $L_{y}=2$ and arbitrary length $L_x = m $ with periodic longitudinal…
We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$…
We present transfer matrices for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and M\"obius strips of the square, triangular, and honeycomb lattices of…
We present exact calculations of the partition function of the q-state Potts model for general q and temperature on strips of the square lattice of width L_y=3 vertices and arbitrary length L_x with periodic longitudinal boundary…
We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and…
We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex square-lattice strip graphs $G$ for a variety of transverse widths $L_t$ and for arbitrarily…
We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary conditions. The general partition function $Z$…
In this paper we present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, for arbitrary temperature on $n$-vertex strip graphs, of width $L_y=2$ and arbitrary length, of the…
We present a set of general results on structural features of the $q$-state Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature Boltzmann variable $v$ for various lattice strips of arbitrarily great width $L_y$…
We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in…
We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for…
We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for self-dual cyclic square-lattice strips of various widths $L_y$ and arbitrarily great lengths $L_x$, with $Q$ and $v$ restricted to satisfy the relation…
We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal…
We present exact calculations of the zero-temperature partition function for the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) for families of arbitrarily long strip graphs of the square and triangular lattices…
We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder graphs with free, cyclic, and M\"obius…
We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the special boundary conditions that are obtained from…
We study the chromatic polynomial P_G(q) for m \times n square- and triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the…