arXiv subjects

Yu. Kozitsky

Publications and source records attributed to Yu. Kozitsky.

5 recordsLinked to original sources

arXiv2025

50 years of Yukhnovskii's critical point theory: its place in the constant flow of theoretical physics

Half a century ago, Ihor Yukhnovskii elaborated a method of studying the critical point of the three-dimensional Ising model based on a layer-by-layer integration in the space of collective variables. His method was an alternative to that based on the $\varepsilon$-expansion for which K. G. Wilson was awarded the Nobel Prize in Physics in 1982. However, Yukhnovskii's technique, which yielded similar results, provided even deeper insight into the nature of this phenomenon. At that time, we, professor's students, saw only this aspect of his theory. Later, I realized that the mentioned Yukhnovskii's work naturally fits into a more general context of the turbulent development of quantum field theory and statistical physics in the last quarter of the twentieth century. The aim of the present article is to look at the main aspects and the impact of Yukhnovskii's theory from this perspective.

cond-mat.stat-mech↗

arXiv2025

Effective and asymptotic scaling in a one-dimensional billiard problem

The emergence of power laws that govern the large-time dynamics of a one-dimensional billiard of $N$ point particles is analysed. In the initial state, the resting particles are placed in the positive half-line $x\geqslant 0$ at equal distances. Their masses alternate between two distinct values. The dynamics is initialized by giving the leftmost particle a positive velocity. Due to elastic inter-particle collisions, the whole system gradually comes into motion, filling both right-hand and left-hand half-lines. As shown by [Chakraborti S., Dhar A., Krapivsky P., SciPost Phys., 2022, 13, 074], an inherent feature of such a billiard is the emergence of two different modes: the shock wave that propagates in $x\geqslant 0$ and the splash region in $x<0$. Moreover, the behaviour of the relevant observables is characterized by universal asymptotic power-law dependencies. In view of the finite size of the system and of finite observation times, these dependencies only start to acquire a universal character. To analyse them, we set up molecular dynamics simulations using the concept of effective scaling exponents, familiar in the theory of continuous phase transitions. We present results for the effective exponents that govern the large-time behaviour of the shock-wave front, the number of collisions, the energies and momentum of different modes and analyse their tendency to approach corresponding universal values.

cond-mat.stat-mech↗

arXiv2011

Motif based hierarchical random graphs: structural properties and critical points of an Ising model

A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, 298, 824-827]. The construction scheme resembles that used in [Hinczewski M., A. Nihat Berker, Phys. Rev. E, 2006, 73, 066126], according to which the short-range bonds are non-random, whereas the long-range bonds appear independently with the same probability. A number of structural properties of the graphs have been described, among which there are degree distributions, clustering, amenability, small-world property. For one of the motifs, the critical point of the Ising model defined on the corresponding graph has been studied.

math-ph↗

arXiv2004

A hierarchical model of quantum anharmonic oscillators: critical point convergence

A hierarchical model of interacting quantum particles performing anharmonic oscillations is studied in the Euclidean approach, in which the local Gibbs states are constructed as measures on infinite dimensional spaces. The local states restricted to the subalgebra generated by fluctuations of displacements of particles are in the center of the study. They are described by means of the corresponding temperature Green (Matsubara) functions. The result of the paper is a theorem, which describes the critical point convergence of such Matsubara functions in the thermodynamic limit.

math-ph↗

arXiv2003

Infinite Order Differential Operators in Spaces of Entire Functions

We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials possessing real nonpositive zeros only and of their uniform limits on compact subsets of the complex plane. We obtain integral representations of some particular cases of these operators and apply these results to obtain explicit solutions to some Cauchy problems for diffusion equations with nonconstant drift term.

math.FA↗