Related papers: Exact solution of the classical dimer model on a t…
On the 1+2 dimensional lattice, we consider a directed polymer in a random Gaussian environment that is independent in time and correlated in space. The spatial correlation is supposed to decay as $(\log |x|)^a /|x|^{2}$, $a>-1$, where the…
We consider the dimer model on the square and hexagonal lattices with doubly periodic weights. The purpose of this paper is threefold: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov (and…
The thermodynamics and dynamics of a one dimensional dimer-forming anharmonic model is studied in the classical limit. This model mimics the behavior of materials with a Peierls instability. Specific heat, correlation length, and order…
We study hard dimers on dynamical lattices in arbitrary dimensions using a random tensor model. The set of lattices corresponds to triangulations of the d-sphere and is selected by the large N limit. For small enough dimer activities, the…
The Kramers-Wannier duality is shown to hold for all the even number spin correlation functions of the two dimensional square lattice Ising model in the sense that the high temperature $(T>T_{c})$ expressions for these correlation functions…
We derive the exact critical couplings ($x^*, y_{\rm a}^*$), where $y_{\rm a}^*/x^* = \sqrt{1+\sqrt2} = 1.533\ldots\,$, for the polymer adsorption transition on the honeycomb lattice, along with the universal critical exponents, from the…
A monomer-dimer reaction lattice model with lateral repulsion among the same species is studied using a mean-field analysis and Monte Carlo simulations. For weak repulsions, the model exhibits a first-order irreversible phase transition…
We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the $S = 1/2$ ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical…
We study the loop $O(n)$ model on the honeycomb lattice. By means of local non-planar deformations of the lattice, we construct a discrete stress-energy tensor. For $n\in [0,2]$, it gives a new observable satisfying a part of Cauchy-Riemann…
Classical Coulomb systems at equilibrium, bounded by a plane dielectric wall, are studied. A general two-point charge correlation function is considered. Valid for any fixed position of one of the points, a new relation is found between the…
Using the monomer-dimer representation of strongly coupled U(N) lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in (2+1) dimensions. A new cluster algorithm allows us to compute…
We solve a class of isoperimetric problems on $\mathbb{R}^2_+ :=\left\{ (x,y)\in \mathbb{R} ^2 : y>0 \right\}$ with respect to monomial weights. Let $\alpha $ and $\beta $ be real numbers such that $0\le \alpha <\beta+1$, $\beta\le 2…
A polymer folding model on the square lattice is constructed with attractive contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a dynamical random lattice, with freely fluctuating co-ordination number at each vertex,…
The classical 1961 solution to the problem of determining the number of perfect matchings (or dimer coverings) of a rectangular grid graph -- due independently to Kasteleyn and to Temperley and Fisher -- consists of changing the sign of…
In this letter we analyze the Hamiltonian formulation of the Jackiw-Teitelboim model of 2D gravity and calculate the central charge associated with the asymptotic symmetries, taking care of boundary terms. For black hole solutions, we show…
We explore topological defects in the 4-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb{Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality…
An asymptotically exact solution is presented for the two-impurity Kondo model for a finite region of the parameter space surrounding the critical point. This region is located in the most interesting intermediate regime where RKKY…
We consider isotropic XY model in the transverse magnetic field on the one dimensional lattice. Another name of the model in Heisenberg XXO model of spin 1/2.We solved long standing problem of evaluation of temperature correlations. We…
We address here a few classical lattice--spin models, involving $n-$component unit vectors ($n=2,3$), associated with a $D-$dimensional lattice $\mathbb{Z}^D,\,D=1,2$, and interacting via a pair potential restricted to nearest neighbours…
Let $K={\bf R}^n\subset {\bf C}^n$ and $Q(x):=\frac{1}{2}\log (1+x^2)$ where $x=(x_1,...,x_n)$ and $x^2 = x_1^2+\cdots +x_n^2$. Utilizing extremal functions for convex bodies in ${\bf R}^n\subset {\bf C}^n$ and Sadullaev's characterization…