Related papers: Exact Potts Model Partition Function on Strips of …
We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions. For free-fermion vertex weights the partition function can be expressed in terms of some Hankel determinant, or equivalently…
We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to…
We study the quench dynamics of the $q$ Potts model on different bi/tri-dimensional lattice topologies. In particular we are interested in instantaneous quenches from $T_i \rightarrow \infty$ to $T \leq T_s$, where $T_s$ is the…
I extend to QCD an efficient method for lattice gauge theory with dynamical fermions. Once the eigenvalues of the Dirac operator and the density of states of pure gluonic configurations at a set of plaquette energies (proportional to the…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
The purpose of this article is to provide a starter kit for multicanonical simulations in statistical physics. Fortran code for the $q$-state Potts model in $d=2, 3,...$ dimensions can be downloaded from the Web and this paper describes…
We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high and low…
The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion method. At low temperatures the specific heat reveals a zero-temperature…
I review recent progress in finite temperature lattice calculations, including calculations of Equation of State, fluctuations of conserved charges and spatial correlation functions. I compare lattice results with the predictions of hadron…
We describe an approach to the study of phase transitions in Potts models based on an estimate of the complexity of the locus of real zeros of the partition function, computed in terms of the classes in the Grothendieck ring of the affine…
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with…
The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions…
The partition function of two-dimensional solitons in a heat bath of mesons is worked out to one-loop. For temperatures large compared to the meson mass, the free energy is dominated by the meson-soliton bound states and the zero modes, a…
The partition functions of ferromagnetic Ising models of square lattices in a finite magnetic field is deduced using topological considerations within a heuristic graph-theoretical approach. These equations are derived separately for low…
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 construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…
The zeros of the size-$n$ partition functions for a statistical mechanical model can be used to help understand the critical behaviour of the model as $n\to\infty$. Here we use weighted Dyck paths as a simple model of two-dimensional…
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…
Sampling from the $q$-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem may be computationally hard, and this hardness…
This paper deals with the location of the complex zeros of the Tutte polynomial for a class of self-dual graphs. For this class of graphs, as the form of the eigenvalues is known, the regions of the complex plane can be focused on the sets…