Related papers: Monomer-dimer model in two-dimensional rectangular…
Discrete fundamental and dipole solitons are constructed, in an exact analytical form, in an array of linear waveguides with an embedded $\mathcal{PT}$-symmetric dimer, which is composed of two nonlinear waveguides carrying equal gain and…
We perform a numerical study of the F-model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size…
We investigate the local density of states of the one-dimensional half-filled spinless fermion model with nearest-neighbor hopping t>0 and interaction V in its Luttinger liquid phase -2t < V <= 2t. The bulk density of states and the local…
Recent developments of the theoretical investigations on the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given for the…
In the past decade, tremendous efforts have been made towards understanding fermionic symmetry protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is…
This paper studies the dimer model on the dual graph of the square-octagon lattice, which can be viewed as the domino tilings with impurities in some sense. In particular, under a certain boundary condition, we give an exact formula…
In the paper we discuss two questions about smooth expanding dynamical systems on the circle. (i) We characterize the sequences of asymptotic length ratios which occur for systems with H\"older continuous derivative. The sequences of…
We calculate the free energy density of the two dimensional O(3) non linear sigma model over a large temperature region. At high temperatures the calculations could be done by perturbation theory whereas in the low temperature regime we…
The dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph $G$ is a union of two dimer covers of $G$. We introduce quaternion weights in the dimer model and show how they can…
Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the…
We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer…
A nonlinear Schr\"odinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schr\"odinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations. We show…
We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a…
Numerical methods are used to examine the thermodynamic characteristics of the two-dimensional Ising model as a function of the number of spins N. Onsager's solution is generalized to a finite-size lattice, and experimentally validated…
Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy $F$ is measured as a…
The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size $L\times M$ and temperature. We start with the dimer method of…
We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrodinger equation (NLS) for the…
We study the $\mathcal{PT} $-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the…
Motivated by the search for best lattice sphere packings in Euclidean spaces of large dimensions we study randomly generated perfect lattices in moderately large dimensions (up to d=19 included). Perfect lattices are relevant in the…
This work presents a Discrete de Rham (DDR) numerical scheme for solving linear elasticity problems on general polyhedral meshes, with a focus on preventing volumetric locking in the quasi-incompressible regime. The method is formulated as…