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Related papers: Transfer Matrices for the Zero-Temperature Potts A…

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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…

Statistical Mechanics · Physics 2009-11-10 Shu-Chiuan Chang , Robert Shrock

We study the chromatic polynomial P_G(q) for m \times n triangular-lattice strips of widths m <= 12_P, 9_F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary…

Statistical Mechanics · Physics 2015-10-08 Jesper Lykke Jacobsen , Jesús Salas , Alan D. Sokal

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…

Statistical Mechanics · Physics 2015-10-08 Jesus Salas , Alan D. Sokal

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…

Statistical Mechanics · Physics 2015-05-13 Shu-Chiuan Chang , Robert Shrock

We present exact solutions for the zero-temperature partition function (chromatic polynomial $P$) and the ground state degeneracy per site $W$ (= exponent of the ground-state entropy) for the $q$-state Potts antiferromagnet on strips of the…

Statistical Mechanics · Physics 2009-10-31 Shu-Chiuan Chang , Robert Shrock

We present exact calculations of the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently the chromatic polynomial) for Moebius strips, with width $L_y=2$ or 3, of regular lattices and homeomorphic…

Statistical Mechanics · Physics 2009-10-31 Robert Shrock

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…

Statistical Mechanics · Physics 2009-10-31 Shu-Chiuan Chang , Robert Shrock

We present exact calculations of the partition function of the $q$-state Potts model on (i) open, (ii) cyclic, and (iii) M\"obius strips of the honeycomb (brick) lattice of width $L_y=2$ and arbitrarily great length. In the infinite-length…

Statistical Mechanics · Physics 2009-10-31 Shu-Chiuan Chang , Robert Shrock

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…

Statistical Mechanics · Physics 2009-10-31 S. -C. Chang , R. Shrock

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…

Statistical Mechanics · Physics 2015-06-24 Jesper Lykke Jacobsen , Jesus Salas

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…

Statistical Mechanics · Physics 2015-05-18 Jesús Salas , Alan D. Sokal

We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graphs of the square lattice with periodic…

Statistical Mechanics · Physics 2009-10-31 Norman Biggs , Robert Shrock

We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary…

Statistical Mechanics · Physics 2008-11-26 Jesper Lykke Jacobsen , Jesus Salas

We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times…

Statistical Mechanics · Physics 2009-11-07 Jesus Salas , Robert Shrock

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 strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc)…

Statistical Mechanics · Physics 2009-11-11 Shu-Chiuan Chang , Robert Shrock

We present exact calculations of the zero-temperature partition function (chromatic polynomial) $P$ for the $q$-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length $L_x$ vertices and of width $L_y=3$…

Statistical Mechanics · Physics 2009-10-31 Shu-Chiuan Chang , Robert Shrock

We present exact calculations of the zero-temperature partition function of the $q$-state Potts antiferromagnet on arbitrarily long strips of the square, triangular, and kagom\'e lattices with width $L_y=2$ or 3 vertices and with periodic…

Statistical Mechanics · Physics 2007-05-23 Robert Shrock , Shan-Ho Tsai

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 $L_y$…

Statistical Mechanics · Physics 2009-11-07 Shu-Chiuan Chang , Robert Shrock

The zero-temperature $q$-state Potts model partition function for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form $P(G,q)=\sum_{j=1}^{N_{G,\lambda}}c_{G,j}(\lambda_{G,j})^{L_x}$, and is equivalent to the…

Statistical Mechanics · Physics 2009-10-31 Shu-Chiuan Chang

We calculate complex-temperature (CT) zeros of the partition function for the $q$-state Potts model on the honeycomb and kagom\'e lattices for several values of $q$. These give information on the CT phase diagrams. A comparison of results…

Statistical Mechanics · Physics 2009-10-30 Heiko Feldmann , Robert Shrock , Shan-Ho Tsai
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