Related papers: Exactly Solvable Lattice Models with Crossing Symm…
We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in…
Recent works have sought to realize certain families of orthogonal, symmetric polynomials as partition functions of well-chosen classes of solvable lattice models. Many of these use Boltzmann weights arising from the trigonometric…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
The solvable $sl(n)$-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed boundary conditions and of two-point…
We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
Strict inequalities in mixed-integer linear optimization can cause difficulties in guaranteeing convergence and exactness. Utilizing that optimal vertex solutions follow a lattice structure we propose a rounding rule for strict inequalities…
We represent a general procedure for calculating the partition function of an Ising model on a one dimensional Fibonacci lattice in presence of magnetic field.This partition function can be written as a sum of partition functions of usual…
For each finite configuration of distinct points in the plane, there is an associated lattice of noncrossing partitions. When these points form the vertices of a convex polygon, the result is the classical noncrossing partition lattice,…
We find and analyse the exact solution of a model of three different polymers with asymmetric contact interactions in two dimensions, modelling a scenario where there are different types of polymers involved. In particular, we find the…
We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…
We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are 1) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, 2) the…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
The hard core model in statistical physics is a probability distribution on independent sets in a graph in which the weight of any independent set I is proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show that…
We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and $XYZ$ model, which is simple to apply for calculation of various correlation functions. We calculate the partition…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being…
Partition functions of certain classes of "spin glass" models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the representation of many such invariants,…