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Related papers: $q$-Plane Zeros of the Potts Partition Function on…

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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

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

The Q-state Potts model can be extended to noninteger and even complex Q in the FK representation. In the FK representation the partition function,Z(Q,a), is a polynomial in Q and v=a-1(a=e^-T) and the coefficients of this…

Statistical Mechanics · Physics 2009-11-07 Seung-Yeon Kim , Richard J. Creswick

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

The properties of the partition function zeros in the complex temperature plane (Fisher zeros) and in the complex $Q$ plane (Potts zeros) are investigated for the $Q$-state Potts model in an arbitrary nonzero external magnetic field $H_q$,…

Statistical Mechanics · Physics 2007-05-23 Seung-Yeon Kim

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 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

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on self-dual strip graphs $G$ of the square lattice with fixed width $L_y$ and arbitrarily great length $L_x$…

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

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the…

Statistical Mechanics · Physics 2009-10-31 H. Feldmann , A. J. Guttmann , I , Jensen , R. Shrock , S. -H. Tsai

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 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 chromatic polynomials (= zero-temperature antiferromagnetic Potts-model partition functions) P_G(q) for m \times n rectangular subsets of the square lattice, with m \le 8 (free or periodic transverse boundary conditions) and n…

Statistical Mechanics · Physics 2015-10-07 Jesús Salas , Alan D. Sokal

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…

Statistical Mechanics · Physics 2009-10-31 Robert 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 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…

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

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

We present exact calculations of the zero-temperature partition function, and ground-state degeneracy (per site), $W$, for the $q$-state Potts antiferromagnet on a variety of homeomorphic families of planar strip graphs $G =…

Statistical Mechanics · Physics 2015-06-25 Robert Shrock , Shan-Ho Tsai

The Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model are studied using the theory of dynamical systems. An exact recurrence relation for the partition function is derived. It is shown that zeros of the partition…

Statistical Mechanics · Physics 2007-05-23 R. G. Ghulghazaryan , N. S. Ananikian

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