arXiv subjects

Vladislav Egorov

Publications and source records attributed to Vladislav Egorov.

6 recordsLinked to original sources

arXiv2025

The generalized density of states in a one-dimensional Ising model with ferrromagnetic and antiferromagnetic interactions

Expressions for the density of states $D(E)$, where $D(E)$ is the number of states of energy $E$, are well known. The present paper offers the expressions for generalized density of states $D_N(E,m)$, where $D_N(E,m)$ is the number of states with energy $E$ and magnetization $m$ in a one-dimensional $N$-spin chain. The expressions obtained here can be considered as reference ones, since all the main characteristics were obtained without them: using the transfer matrix technique or using well-known expressions for the density of states $D(E)=\sum_m{D_N(E,m)}$. Nevertheless, the knowledge of quantity $D_N(E,m)$ helps to understand the model properties and allows the analysis of the temporal behavior of magnetization $m=m(τ)$. In particular, we demonstrate that in a one-dimensional model spontaneous magnetization can be observed at a non-zero temperature. However, the spontaneous magnetization can randomly change its sign, which results in the magnetization averaged over a very long observation period becoming zero $\langle m(τ)\rangle$.

cond-mat.dis-nn↗

arXiv2025

Analytic expressions for estimation of the critical properties of inhomogeneous Ising models

In many applications of spin models, the fast estimation of their critical temperatures and other physical properties is of great importance. In this work, we present the analytical expressions estimating the critical properties of inhomogeneous Ising models with ferromagnetic interactions. The expressions were obtained within the framework of the m-vicinity method. The accuracy of the critical temperature estimations was evaluated through comparison with Monte Carlo simulations. Special attention was given to the case when the model consists of two interacting interpenetrating homogeneous sublattices, and relationships for the compositional dependence of the critical temperature were derived.

cond-mat.stat-mech↗

arXiv2024

Density Function of Weighted Sum of Chi-Square Variables with Trigonometric Weights

We have investigated a weighted chi-square distribution of the variable $ξ$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $ϕ_k=2πk/N$, where $k \in \{0,1,...,N-1\}$ and $N$ is the number of the freedom degrees. We have found the exact expression for the density function of this distribution and its approximation for large $N$. The distribution is compared with the Gaussian distribution.

cond-mat.dis-nn↗

arXiv2024

The Accuracy and Performance Analysis of the 1/t Wang-Landau Algorithm in the Joint Density of States Estimation

The 1/t Wang-Landau algorithm is analyzed from the viewpoint of execution time and accuracy when it is used in computations of the density of states of a two-dimensional Ising model. We find that the simulation results have a systematic error, the magnitude of which decreases with increasing the lattice size. The relative error has two maxima: the first one is located near the energy of the ground state, and the second maximum corresponds to the value of the internal energy at the critical point. We demonstrate that it is impossible to estimate the execution time of the 1/t Wang-Landau algorithm in advance when simulating large lattices. The reason is that the criterion for switching to the 1/t mode was not met when the final value of the modification factor was reached. The simultaneous calculations of the density of states for energy and magnetization are shown to lead to higher accuracy in estimating statistical moments of internal energy.

cond-mat.dis-nn↗

arXiv2021

Analytical solutions for Ising models on high dimensional lattices

We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions d>=3. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be used when calculating the free energy. When we account for interaction with the nearest neighbors only, the value of this parameter depends on the dimension of the lattice d. We obtain an expression for the critical temperature in terms of the interaction constants that is in a good agreement with results of computer simulations. For d=5, 6, 7, our theoretical estimates match the experiments both qualitatively and quantitatively. For d=3, 4, our method is sufficiently accurate for calculation of the critical temperatures, however, it predicts a finite jump of the heat capacity at the critical point. In the case of the three-dimensional lattice (d=3), this contradicts to the commonly accepted ideas of the type of the singularity at the critical point. For the four-dimensional lattice (d = 4) the character of the singularity is under current discussion. For the dimensions d=1, 2 the m-vicinity method is not applicable.

cond-mat.dis-nn↗

arXiv2020

Stochastic Fluid Dynamics Simulations of the Velocity Distribution in Protoplasmic Streaming

Protoplasmic streaming in plant cells is directly visible in the cases of \textit{Chara corallina} and \textit{Nitella flexilis}, and this streaming is understood to play a role in the transport of biological materials. For this reason, related studies have focused on molecular transportation from a fluid mechanics viewpoint. However, the experimentally observed distribution of the velocity along the flow direction $x$, which exhibits two peaks at $V_x\!=\!0$ and at a finite $V_x(\not=\!0)$, remains to be studied. In this paper, we numerically study whether this behavior of the flow field can be simulated by a 2D stochastic Navier-Stokes (NS) equation for Couette flow, in which random Brownian force is assumed. We present the first numerical evidence that these peaks are reproduced by the stochastic NS equation, which implies that the Brownian motion of the fluid particles plays an essential role in the emergence of these peaks in the velocity distribution. We also find that the position of the peak at $V_x(\not=\!0)$ moves with the variation in the strength $D$ of the random Brownian force, which also changes depending on physical parameters such as the kinematic viscosity, boundary velocity and diameter of the plant cells.

cond-mat.stat-mech↗