Related papers: Exactly Solvable Lattice Models with Crossing Symm…
We consider partition functions on the $N\times N$ square lattice with the local Boltzmann weights given by the $R$-matrix of the $U_{t}(\widehat{sl}(n+1|m))$ quantum algebra. We identify boundary states such that the square lattice can be…
Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topological excitations have low energies. The low energy properties…
Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…
In our previous paper [H. K., J.Stat.Mech.(2015) P08020], we investigated an interacting-particle model with infinite-range cosine potentials, and derived the partition function which shows solid-fluid phase transition by exact calculation.…
In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…
In this succinct note, it is showed that a partition function of equivalent classes of hyperbolic surfaces can be connected to an Ising model located on the boundary of the Poincare disc, as hinted by Poincare's Uniformization theorem and…
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary…
We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter $\lambda$, each matching $M$ is assigned a weight $\lambda^{|M|}$. The counting…
An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the…
Starting from the operator algebra of the (1+1)D Ising model on a spatial lattice, this paper explicitly constructs a subalgebra of smooth operators that are natural candidates for continuum fields in the scaling limit. At the critical…
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with…
A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest neighbor interactions, the vertices defining the model also interact alongone of the diagonals of the lattice. Such family of…
We determine properties of the lattice Boltzmann method for semiclassical fluids, which is based on the Boltzmann equation and the equilibrium distribution function is given either by the Bose-Einstein or the Fermi-Dirac ones. New…
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact…
Analytical solutions to the lattice Boltzmann Equation make it possible to study the method itself, explore the properties of its collision operator, and identify implementations of boundary conditions. In this paper, we propose a method to…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. Focusing on lower-dimensional lattice systems with more modest resource…
We introduce a novel mesoscopic computational model based on a multiphase-multicomponent lattice Boltzmann method for the simulation of self-phoretic particles in the presence of liquid-liquid interfaces. Our model features fully resolved…
By taking the freezing limit of a spin Calogero-Sutherland model containing `anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This…
We study random one-Lipschitz integer functions $f$ on the vertices of a finite connected graph, sampled according to the weight $W(f) = \prod_{\langle v, w \rangle \in E} \mathbf{c}^{ \mathbb{I} \{ f(v) = f(w) \} }$ where $\mathbf{c} \geq…