Related papers: Transfer Matrices and Partition-Function Zeros for…
We revisit the problem of Q-colourings of the triangular lattice using a mapping onto an integrable spin-one model, which can be solved exactly using Bethe Ansatz techniques. In particular we focus on the low-energy excitations above the…
We present an analysis of the structure and properties of chromatic polynomials $P(G_{pt,\vec m},q)$ of one-parameter and multi-parameter families of planar triangulation graphs $G_{pt,\vec m}$, where ${\vec m} = (m_1,...,m_p)$ is a vector…
We calculate the chromatic polynomials $P$ for $n$-vertex strip graphs of the form $J(\prod_{\ell=1}^m H)I$, where $J$ and $I$ are various subgraphs on the left and right ends of the strip, whose bulk is comprised of $m$-fold repetitions of…
The purpose of the present paper is to provide, for all pairs of integers $(\Delta,g)$ with $\D\ge 3$ and $g\ge 3$, a positive number $C(\Delta, g)$ such that chromatic polynomial $P_G(q)$ of a graph $G$ with maximum degree $\Delta$ and…
We study a square-lattice three-state Potts antiferromagnet with a staggered polarization field at finite temperature. Numerically treating the transfer matrices, we determine two phase boundaries separating the model-parameter space into…
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 =…
We consider proper colorings of planar graphs embedded in the annulus, such that vertices on one rim can take Q_s colors, while all remaining vertices can take Q colors. The corresponding chromatic polynomial is related to the partition…
We present exact results on the partition function of the $q$-state Potts model on various families of graphs $G$ in a generalized external magnetic field that favors or disfavors spin values in a subset $I_s = \{1,...,s\}$ of the total set…
The microcanonical transfer matrix and its extensions offer a new way of obtaining exact partition functions on finite two dimensional lattices. We show the density of the partition function zeros in the complex x- plane for the Ising model…
The $Q$-state Potts model on the simple-cubic lattice is studied using the zeros of the exact partition function on a finite lattice. The critical behavior of the model in the ferromagnetic and antiferromagnetic phases is discussed based on…
We study the antiferromagnetic $q$-state Potts model on the square lattice for $q=3$ and $q=4$, using the Wang-Swendsen-Koteck\'y Monte Carlo algorithm and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good control up…
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 $L_y$…
In this talk we report on our study of two-colour lattice QCD with N_f=4 staggered fermion degrees of freedom with equal electric charge q in a homogeneous magnetic field B at non-zero temperature T. We find indications for a non-monotonic…
We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong…
We show an exact equivalence of the free energy of the $q$-state Potts antiferromagnet on a lattice $\Lambda$ for the full temperature interval $0 \le T \le \infty$ and the free energy of the $q$-state Potts model on the dual lattice for a…
We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit,…
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…
Given an infinite graph $\GI$ quasi-transitive and amenable with maximum degree $\D$, we show that reduced ground state degeneracy per site $W_r(\GI,q)$ of the q-state antiferromagnetic Potts model at zero temperature on $\GI$ is analytic…
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…
The chromatic polynomial P_G(q) of a loopless graph G is known to be nonzero (with explicitly known sign) on the intervals (-\infty,0), (0,1) and (1,32/27]. Analogous theorems hold for the flow polynomial of bridgeless graphs and for the…