Related papers: Exact Potts Model Partition Functions on Ladder Gr…
We study the Potts model (defined geometrically in the cluster picture) on finite two-dimensional lattices of size L x N, with boundary conditions that are free in the L-direction and periodic in the N-direction. The decomposition of the…
We discuss a new class of identities between correlation functions which arise from a local Z_2 invariance of the partition function of the q-state Potts model on general graphs or lattices. Their common feature is to relate the thermal…
We study the partition function per site of the integrable $Sp(2n)$ vertex model on the square lattice. We establish a set of transfer matrix fusion relations for this model. The solution of these functional relations in the thermodynamic…
In this paper, we introduce a novel and general method for computing partition functions of solvable lattice models with free fermionic Boltzmann weights. The method is based on the ``permutation graph'' and the ``$F$-matrix'': the…
Since the grand partition function $Z_q$ for the so-called $q$-particles (i.e.,\ quons), $q\in(-1,1)$, cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for $q=0$, and its…
We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the…
The Yang-Lee zeros of the Q-state Potts model are investigated in 1, 2 and 3 dimensions. Analytical results derived from the transfer matrix for the one-dimensional model reveal a systematic behavior of the locus of zeros as a function of…
We derive a closed-form combinatorial expression for the number of states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach…
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…
We consider a refined version of the string-net model which assigns a different energy cost to each plaquette excitation. Using recent exact calculations of the energy-level degeneracies we compute the partition function of this model and…
We present exact calculations of the zero-temperature partition function $Z(G,q,T=0)$ and ground-state degeneracy $W(\{G\},q)$ for the $q$-state Potts antiferromagnet on a number of families of graphs $G$ for which (generalizing $q$ from…
In this paper, we consider an extended Kazakov-Migdal model defined on an arbitrary graph. The partition function of the model, which is expressed as the summation of all Wilson loops on the graph, turns out to be represented by the…
In this article we create a new algorithm for the perfect simulation of the infinite Potts model at a sufficiently small or at a sufficiently high temperature, in particular under the transition phase temperature. We study the model for…
The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on MxN square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa),…
We study the partition function and free energy of the Curie-Weiss model with complex temperature, and partially describe its phase transitions. As a consequence, we obtain information on the locations of zeros of the partition function.
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $q$-state Potts model to order $z^{56}$ (i.e. $u^{28}$), $z^{47}$, $z^{43}$,…
A phenomenological approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts…
We present a large $q$ expansion of the 2d $q$-states Potts model free energies up to order 9 in $1/\sqrt{q}$. Its analysis leads us to an ansatz which, in the first-order region, incorporates properties inferred from the known critical…
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Neto\v{c}n\'y and Redig and the cluster expansion approach…
We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group $G$ on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules…