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Vladimir V. Papoyan

Publications and source records attributed to Vladimir V. Papoyan.

6 recordsLinked to original sources
arXiv2025

Exact finite-size corrections in the dimer model on a cylinder

The exact finite-size corrections to the free energy $F$ of the dimer model on lattice $\mathcal{M} \times \mathcal{N}$ with cylindrical boundary conditions have been derived for three cases where the lattice is completely covered by dimers: $\mathcal{M} = 2M$, $\mathcal{N} = 2N$; $\mathcal{M} = 2M - 1$, $\mathcal{N} = 2N$; and $\mathcal{M} = 2M$, $\mathcal{N} = 2N - 1$. For these types of cylinders, ratios $r_p(ρ)$ of the $p$th coefficient of $F$ have been calculated for the infinitely long cylinder (${\mathcal M} \rightarrow \infty$) and infinitely long strip (${\mathcal N} \rightarrow \infty$) at varying aspect ratios. As in previous studies of the dimer model on the rectangular lattice with free boundary conditions and for the Ising model with Brascamp-Kunz boundary conditions, the limiting values $p \to \infty$ exhibit abrupt anomalous behaviour of ratios $r_p(ρ)$ at certain values of $ρ$. These critical values of $ρ$ and the limiting values of the finite-size expansion coefficient ratios vary between the different models.

cond-mat.stat-mech↗
arXiv2024

Logarithmic negativity of the 1D antiferromagnetic spin-1 Heisenberg model with single-ion anisotropy

We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field B and single-ion anisotropy D on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement LN. Our main result is the disappearance of LN both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low temperature states. Such disappearance occurs at a critical value of B and D. The resulting phase diagram for the behaviour of LN is discussed in the B - D plane, including a separating line - ending in a triple point - where the energy density is independent on the size. Finally, results for LN at finite temperature as a function of B and D are presented and commented.

cond-mat.stat-mech↗
arXiv2023

Exact coefficients of finite-size corrections in the Ising model with Brascamp-Kunz boundary conditions and their relationships for strip and cylindrical geometries

We derive exact finite-size corrections for the free energy $F$ of the Ising model on the ${\cal M} \times 2 {\cal N}$ square lattice with Brascamp-Kunz boundary conditions. We calculate ratios $r_p(ρ)$ of $p$th coefficients of F for the infinitely long cylinder (${\cal M} \to \infty$) and the infinitely long Brascamp-Kunz strip (${\cal N} \to \infty$) at varying values of the aspect ratio $ρ={(\cal M}+1) / 2{\cal N}$. Like previous studies have shown for the two-dimensional dimer model, the limiting values $p \to \infty$ of $r_p(ρ)$ exhibit abrupt anomalous behaviour at certain values of $ρ$. These critical values of $ρ$ and the limiting values of the finite-size-expansion-coefficient ratios differ, however, between the two models.

cond-mat.stat-mech↗
arXiv2022

The sub-diffusive behavior of chromatin in changing environment

The rotor-router walk model is proposed to describe the sub-diffusive behavior of double-strand breaks in chromatin caused by external factors such as heavy ions, $γ$-irradiation, etc. The mechanism of the double-strand breaks reparation is considered in terms of this model.

cond-mat.stat-mech↗
arXiv2019

Exact finite-size corrections in the dimer model on a planar square lattice

We consider the dimer model on the rectangular $2M \times 2N$ lattice with free boundary conditions. We derive exact expressions for the coefficients in the asymptotic expansion of the free energy in terms of the elliptic theta functions ($θ_2, θ_3, θ_4$) and the elliptic integral of second kind ($E$), up to 22nd order. Surprisingly we find that ratio of the coefficients $f_p$ in the free energy expansion for strip ($f_p^\mathrm{strip}$) and square ($f_p^\mathrm{sq}$) geometries $r_p={f_p^\mathrm{strip}}/{f_p^\mathrm{sq}}$ in the limit of large $p$ tends to $1/2$. Furthermore, we predict that the ratio of the coefficients $f_p$ in the free energy expansion for rectangular ($f_p(ρ)$) for aspect ratio $ρ> 1$ to the coefficients of the free energy for square geometries, multiplied by $ρ^{-p-1}$, that is $r_p=ρ^{-p-1} {f_p(ρ)}/{f_p^\mathrm{sq}}$, is also equal to $1/2$ in the limit of $p \to \infty$. We find that the corner contribution to the free energy for the dimer model on rectangular $2M \times 2N$ lattices with free boundary conditions is equal to zero and explain that result in the framework of conformal field theory, in which the central charge of the considering model is $c=-2$. We also derive a simple exact expression for the free energy of open strips of arbitrary width.

cond-mat.stat-mech↗