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Yurij Holovatch

Publications and source records attributed to Yurij Holovatch.

At least 19 recordsLinked to original sources
arXiv2026

The Lee-Yang property of the Blume-Capel model

The Lee-Yang theory is based on the theorem concerning a property of the ferromagnetic Ising model partition function proved by T. D. Lee and C. N. Yang in 1952. It provides powerful tools for understanding the very nature of phase transitions and critical phenomena in various spin and similar models. Sometimes, this theory is applied to models for which the theorem's validity has not been proved. By the main result of E. H. Lieb and A. D. Sokal, Commun. Math. Phys. 80, 153 (1981), for a given ferromagnetic model, this validity is guaranteed by the same property of the single-spin partition function. Due to the anisotropy term $\sum_i \Delta S_i^2$, the single-spin partition function of the Blume-Capel model fails to have the Lee-Yang property for $\beta \Delta> \ln 2$. In this article, we show that the ferromagnetic interaction in such a model can induce the Lee-Yang property, even for these values of $\beta \Delta$. To the best of our knowledge, it is the first result of this kind.

math-ph↗
arXiv2026

Staggering domino-like blast front motion in a one-dimensional cold gas

One-dimensional alternating particle systems are widely used to study interconnections between the hydrodynamics of blast waves in a gas-like medium and the Newtonian dynamics of its corpuscular constituents. We study the model in which point particles with masses $m,\mu, m,\mu,\dots, (m\geq\mu)$ are distributed on the positive half-line $\mathbb{R}_{+}$. Their dynamics are initiated by giving a positive velocity to the leftmost particle; in its course, the particles undergo elastic collisions. For this model with $m/\mu=2$, it has previously been established that the dynamics that start from random initial positions are consistent with predictions based on Euler's hydrodynamic equation. In particular, they have the following properties: (i) the position of the rightmost particle (shock front) evolves as $t^\delta$ with $\delta<1$; (ii) recoiled particles behind the front enter the negative half-axis; (iii) particles with locations $x\leq0$ move ballistically and eventually take over the total energy of the system. In this paper, we present numerical and analytical results for the dynamics of this model with nonrandom (typically equidistant) initial positions and various values of $m/\mu$. For $m/\mu=2$ and equidistant initial positions, our results qualitatively agree with those just mentioned. At the same time, we found an infinite family of numbers $\{\mathcal{M}_k\}$ such that, for $m/\mu=\mathcal{M}_k$, the hydrodynamic behavior mentioned changes drastically to the following. At each moment, only a single triplet $m,\mu, m$ is in motion, whereas all other particles are at rest. As a result, the shock front moves ballistically with an average velocity equal to the initial one. Such a `staggering domino-like' picture is obtained as an exact solution, which yields, in particular, explicit formulas for $\mathcal{M}_k$ and the particle velocities and positions.

cond-mat.stat-mech↗
arXiv2025

Breakdown of hydrodynamics in a one-dimensional cold gas

The following model is studied analytically and numerically: point particles with masses $m,\mu,m, \dots$ ($m\geq\mu$) are distributed over the positive half-axis. Their dynamics is initiated by giving a positive velocity to the particle located at the origin; in its course the particles undergo elastic collisions. We show that, for certain values of $m/\mu$, starting from the initial state where the particles are equidistant the system evolves in a hydrodynamic way: (i) the rightmost particle (blast front) moves as $t^{\delta}$ with $\delta < 1$; (ii) recoiled particles behind the front enter the negative half-axis; (iii) the splatter -- the particles with locations $x\leq 0$ -- moves in the ballistic way and eventually takes over the whole energy of the system. These results agree with those obtained in S. Chakraborti et al, SciPost Phys. 2022, 13, 074, for $m/\mu=2$ and random initial particle positions. At the same time, we explicitly found the collection of positive numbers $\{\mathcal{M}_i, i \in \mathbf{N} \}$ such that, for $m/\mu = \mathcal{M}_i$, $i\leq 700$, the following holds: (a) the splatter is absent; (b) the number of simultaneously moving particles is at most three; (c) the blast front moves in the ballistic way. However, if, similarly as in S. Chakraborti et al, the particle positions are sampled from a uniformly distributed ensemble, for $m/\mu = \mathcal{M}_i$ the system evolves in a hydrodynamic way.

cond-mat.stat-mech↗
arXiv2025

Partition function zeros for the Blume-Capel model on a complete graph

In this paper we study finite-size effects in the Blume-Capel model through the analysis of the zeros of the partition function. We consider a complete graph and make use of the behaviour of the partition function zeros to elucidate the crossover from effective to asymptotic properties. While in the thermodynamic limit the exact solution yields the asymptotic mean-field behaviour, for finite system sizes an effective critical behaviour is observed. We show that even for large systems, the criticality is not asymptotic. We also present insights into how partition function zeros in different complex fields (temperature, magnetic field, crystal field) give different precision and provide us with different parts of the larger picture. This includes the differences between criticality and tricriticality as seen through the lens of Fisher, Lee-Yang, and Crystal Field zeros.

cond-mat.stat-mech↗
arXiv2024

Collective decision-making with heterogeneous biases: Role of network topology and susceptibility

The ability of groups to make accurate collective decisions depends on a complex interplay of various factors, such as prior information, biases, social influence, and the structure of the interaction network. Here, we investigate a spin model that accounts for heterogeneous preferences and enables control over the non-linearity of social interactions. Building on previous results for complete graphs and regular 2D lattices, we investigate how the modification of network topology towards (sparse) random graphs can affect collective decision-making. We use two different measures of susceptibility to assess the responsiveness of the system to internal and external perturbations. In particular, we investigate how the maximum of susceptibility depends on network connectivity. Based on our findings, we discuss how collective systems might adapt to changes in environmental fluctuations by adjusting their network structure or the nature of their social interactions in order to remain in the region of maximal susceptibility.

physics.soc-ph↗
arXiv2024

Julian Hirniak, an early proponent of periodic chemical reaction

In this article we present and discuss the work and scientific legacy of Julian Hirniak, the Ukrainian chemist and physicist who published two articles in 1908 and 1911 about periodic chemical reactions. Over the last 110+ years, his theoretical work has often been cited favorably in connection with Alfred Lotka's theoretical model of an oscillating reaction system. Other authors have pointed out thermodynamic problems in Hirniak's reaction scheme. Based on English translations of his 1908 Ukrainian and 1911 German articles, we show that Hirniak's claim (that a cycle of inter-conversions of three chemical isomers in a closed reaction vessel can show damped periodic behavior) violates the \textit{Principle of Detailed Balance} (i.e., the Second Law of Thermodynamics), and that Hirniak was aware of this Principle. We also discuss his results in relation to Lotka's first model of damped oscillations in an open system of chemical reactions involving an auto-catalytic reaction operating far from equilibrium. Taking hints from both Hirniak and Lotka, we show that the mundane case of a kinase enzyme catalyzing the phosphorylation of a sugar can satisfy Hirniak's conditions for damped oscillations to its steady state flux (i.e., the Michaelis--Menten rate law), but that the oscillations are so highly damped as to be unobservable. Finally, we examine historical and factual misunderstandings related to Julian Hirniak and his publications.

physics.hist-ph↗
arXiv2024

Ising's roots and the transfer-matrix eigenvalues

Today, the Ising model is an archetype describing collective ordering processes. And, as such, it is widely known in physics and far beyond. Less known is the fact that the thesis defended by Ernst Ising 100 years ago (in 1924) contained not only the solution of what we call now the `classical 1D Ising model' but also other problems. Some of these problems, as well as the method of their solution, are the subject of this note. In particular, we discuss the combinatorial method Ernst Ising used to calculate the partition function for a chain of elementary magnets. In the thermodynamic limit, this method leads to the result that the partition function is given by the roots of a certain polynomial. We explicitly show that `Ising's roots' that arise within the combinatorial treatment are also recovered by the eigenvalues of the transfer matrix, a concept that was introduced much later. Moreover, we discuss the generalization of the two-state model to a three-state one presented in Ising's thesis, but not included in his famous paper of 1925 (E. Ising, Z.Physik 31 (1925) 253). The latter model can be considered as a forerunner of the now abundant models with many-component order parameters.

physics.hist-ph↗
arXiv2024

Critical and tricritical singularities from small-scale Monte Carlo simulations: The Blume-Capel model in two dimensions

We show that the study of critical properties of the Blume-Capel model at two dimensions can be deduced from Monte Carlo simulations with good accuracy even for small system sizes when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins! We also show that the zeros are very sensitive to subtle crossover effects.

cond-mat.stat-mech↗
arXiv2023

The diaspora model for human migration

Migration's impact spans various social dimensions, including demography, sustainability, politics, economy and gender disparities. Yet, the decision-making process behind migrants choosing their destination remains elusive. Existing models primarily rely on population size and travel distance to explain flow fluctuations, overlooking significant population heterogeneities. Paradoxically, migrants often travel long distances and to smaller destinations if their diaspora is present in those locations. To address this gap, we propose the diaspora model of migration, incorporating intensity (the number of people moving to a country) and assortativity (the destination within the country). Our model considers only the existing diaspora sizes in the destination country, influencing the probability of migrants selecting a specific residence. Despite its simplicity, our model accurately reproduces the observed stable flow and distribution of migration in Austria (postal code level) and US metropolitan areas, yielding precise estimates of migrant inflow at various geographic scales. Given the increase in international migrations due to recent natural and societal crises, this study enlightens our understanding of migration flow heterogeneities, helping design more inclusive, integrated cities.

physics.soc-ph↗
arXiv2023

Individual bias and fluctuations in collective decision making: from algorithms to Hamiltonians

In this paper, we reconsider the spin model suggested recently to understand some features of collective decision making among higher organisms [A.T. Hartnett et al., Phys. Rev. Lett. 116 (2016) 038701]. Within the model, the state of an agent $i$ is described by the pair of variables corresponding to its opinion $S_i=\pm 1$ and a bias $\omega_i$ towards any of the opposing values of $S_i$. Collective decision making is interpreted as an approach to the equilibrium state within the non-linear voter model subject to a social pressure and a probabilistic algorithm. Here, we push such physical analogy further and give the statistical physics interpretation of the model, describing it in terms of the Hamiltonian of interaction and looking for the equilibrium state via explicit calculation of its partition function. We show that depending on the assumptions about the nature of social interactions two different Hamiltonians can be formulated, which can be solved with different methods. In such an interpretation the temperature serves as a measure of fluctuations, not considered before in the original model. We find exact solutions for the thermodynamics of the model on the complete graph. The general analytical predictions are confirmed using individual-based simulations. The simulations allow us also to study the impact of system size and initial conditions in the collective decision making in finite-sized systems, in particular with respect to convergence to metastable states.

cond-mat.stat-mech↗
arXiv2023

Potts Model with Invisible States: A Review

The Potts model with invisible states was introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where $Z_q$ symmetry is spontaneously broken. It differs from the ordinary $q$-state Potts model in that each spin, besides the usual $q$ visible states, can be also in any of $r$ so-called invisible states. Spins in an invisible state do not interact with their neighbours but they do contribute to the entropy of the system. As a consequence, an increase in $r$ may cause a phase transition to change from second to first order. Potts models with invisible states describe a number of systems of interest in physics and beyond and have been treated by various tools of statistical and mathematical physics. In this paper we aim to give a review of this fundamental topic.

cond-mat.stat-mech↗
arXiv2022

On the new universality class in structurally disordered $n$-vector model with long-range interactions

We study a stability border of a region where nontrivial critical behaviour of an $n$-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g. weak quenched dilution). This border is given by the marginal dimension of the order parameter $n_c$ dependent on space dimension, $d$, and a control parameter of the interaction decay, $\sigma$, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field-theoretical renormalization group results for the pure model with long-range interactions we get $n_c$ as a three loop $\epsilon=2\sigma-d$-expansion. We provide numerical values for $n_c$ applying series resummation methods. Our results show that not only the Ising systems ($n=1$) can belong to the new disorder-induced long-range universality class at $d=2$ and $d=3$.

cond-mat.stat-mech↗
arXiv2022

Effective and asymptotic criticality of structurally disordered magnets

Changes in magnetic critical behaviour of quenched structurally-disordered magnets are usually exemplified in experiments and in MC simulations by diluted systems consisting of magnetic and non-magnetic components. By our study we aim to show, that similar effects can be observed not only for diluted magnets with non-magnetic impurities, but may be implemented, e.g., by presence of two (and more) chemically different magnetic components as well. To this end, we consider a model of the structurally-disordered quenched magnet where all lattice sites are occupied by Ising-like spins of different length $L$. In such random spin length Ising model the length $L$ of each spin is a random variable governed by the distribution function $p(L)$. We show that this model belongs to the universality class of the site-diluted Ising model. This proves that both models are described by the same values of asymptotic critical exponents. However, their effective critical behaviour differs. As a case study we consider a quenched mixture of two different magnets, with values of elementary magnetic moments $L_1=1$ and $L_2=s$, and of concentration $c$ and $1-c$, correspondingly. We apply field-theoretical renormalization group approach to analyze the renormalization group flow for different initial conditions, triggered by $s$ and $c$, and to calculate effective critical exponents further away from the fixed points of the renormalization group transformation. We show how the effective exponents are governed by difference in properties of the magnetic components.

cond-mat.dis-nn↗
arXiv2022

Phase transitions above the upper critical dimension

These lecture notes provide an overview of the renormalization group (RG) as a successful framework to understand critical phenomena above the upper critical dimension $d_{\rm uc}$. After an introduction to the scaling picture of continuous phase transitions, we discuss the apparent failure of the Gaussian fixed point to capture scaling for Landau mean-field theory, which should hold in the thermodynamic limit above $d_{\rm uc}$. We recount how Fisher's dangerous-irrelevant-variable formalism applied to thermodynamic functions partially repairs the situation but at the expense of hyperscaling and finite-size scaling, both of which were, until recently, believed not to apply above $d_{\rm uc}$. We recall limitations of various attempts to match the RG with analytical and numerical results for Ising systems. We explain how the extension of dangerous irrelevancy to the correlation sector is key to marrying the above concepts into a comprehensive RG scaling picture that renders hyperscaling and finite-size scaling valid in all dimensions. We collect what we believe is the current status of the theory, including some new insights and results. This paper is in grateful memory of Michael Fisher who introduced many of the concepts discussed and who, half a century later, contributed to their advancement.

cond-mat.stat-mech↗
arXiv2022

Schottky's forgotten step to the Ising model

A longstanding problem in natural science and later in physics was the understanding of the existence of ferromagnetism and its disappearance under heating to high temperatures. Although a qualitative description was possible by the Curie-Weiss theory it was obvious that a microscopic model was necessary to explain the tendency of the elementary magnetons to prefer parallel ordering at low temperatures. Such a model was proposed in 1922 by W. Schottky within the old Bohr-Sommerfeld quantum mechanics and claimed to explain the high values of the Curie temperatures of certain ferromagnets. Based on this idea Ising formulated a new model for ferromagnetism in solids. Simultaneously the old quantum mechanics was replaced by new concepts of Heisenberg and Schr\"odinger and the discovery of spin. Thus Schottky's idea was outperformed and finally replaced in 1928 by Heisenberg exchange interaction. This led to a reformulation of Ising's model by Pauli at the Solvay conference in 1930. Nevertheless one might consider Schottky's idea as a forerunner of this development explaining and asserting that the main point is the Coulomb energy leading to the essential interaction of neighboring elementary magnets.

physics.hist-ph↗
arXiv2022

Network analysis of the Kyiv bylyny cycle -- east Slavic epic narratives

In recent times, the advent of network science permitted new quantitative approaches to literary studies. Here we bring the Kyiv bylyny cycle into the field - East Slavic epic narratives originating in modern-day Ukraine. By comparing them to other prominent European epics, we identify universal and distinguishing properties of the social networks in bylyny. We analyse community structures and rank the most important characters. The method allows to bolster hypotheses from humanities literature - such as the position of Prince Volodymyr - and to generate new ones We show how the Kyiv cycle of bylyny fits very well with narrative networks from other nations - especially heroic ones. We anticipate that, besides delivering new narratological insights, this study will aid future scholars and interested public to navigate their way through Ukraine's epic story and identify its heroes.

physics.soc-ph↗
arXiv2022

Big fish and small ponds: why the departmental h-index should not be used to rank universities

The size-dependent nature of the so-called group or departmental h-index is reconsidered in this paper. While the influence of unit size on such collective measures was already demonstrated a decade ago, institutional ratings based on this metric can still be found and still impact on the reputations and funding of many research institutions. The aim of this paper is to demonstrate the fallacy of this approach to collective research-quality assessment in a simple way, focusing on the h-index in its original form. We show that randomly reshuffling real scientometric data (varying numbers of citations) amongst institutions of varying size, while maintaining the volume of their research outputs, has little effect on their departmental h-index. This suggests that the relative position in ratings based on the collective h-index is determined not only by quality (impact) of particular research outputs but by their volume. Therefore, the application of the collective h-index in its original form is disputable as a basement for comparison at aggregated levels such as to research groups, institutions or journals. We suggest a possible remedy for this failing which is implementable in a manner that is as simple and understandable as the h-index itself.

cs.DL↗