arXiv subjects

Yu. Holovatch

Publications and source records attributed to Yu. Holovatch.

At least 37 records · Page 2Linked to original sources

arXiv2016

Universal free-energy distribution in the critical point of a random Ising ferromagnet

We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions D <4, we derive an explicit expression for the probability distribution function (PDF) of the critical free energy fluctuations. In particular, using known fixed-point values for the renormalized coupling parameters, we obtain the universal curve for such PDF in the dimension D=3. It is demonstrated that this function is strongly asymmetric: its left tail is much slower than the right one.

cond-mat.stat-mech↗

arXiv2015

On the discontinuity of the specific heat of the Ising model on a scale-free network

We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay $P(K)\sim K^{-λ}$. It is well established that the model is characterized by classical mean-field exponents for $λ>5$. In this note we show that the specific-heat discontinuity $δc_h$ at the critical point remains $λ$-dependent even for $λ>5$: $δc_h=3(λ-5)(λ-1)/[2(λ-3)^2]$ and attains its mean-field value $δc_h=3/2$ only in the limit $λ\to \infty$. We compare this behaviour with recent measurements of the $d$ dependency of $δc_h$ made for the Ising model on lattices with $d>4$ [Lundow P.H., Markström K., Nucl. Phys. B, 2015, Vol. 895, 305].

cond-mat.stat-mech↗

arXiv2015

Marginal dimensions of the Potts model with invisible states

We reconsider the mean-field Potts model with $q$ interacting and $r$ non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the $Z_q$-symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of $r$ at which the order of the phase transition changes. In the $q=2$ case, we determine that value to be $r_c = 3.65(5)$; there is a second-order phase transition there when $r r_c$. We also analyse the region $1 \leq q<2$ and show that the change from second to first order there is manifest through a new mechanism involving {\emph{two}} marginal values of $r$. The $q=1$ limit gives bond percolation and some intermediary values also have known physical realisations. Above the lower value $r_{c1}$, the order parameters exhibit discontinuities at temperature $\tilde{t}$ below a critical value $t_c$. But, provided $r>r_{c1}$ is small enough, this discontinuity does not appear at the phase transition, which is continuous and takes place at $t_c$. The larger value $r_{c2}$ marks the point at which the phase transition at $t_c$ changes from second to first order. Thus, for $r_{c1}< r < r_{c2}$, the transition at $t_c$ remains second order while the order parameter has a discontinuity at $\tilde{t}$. As $r$ increases further, $\tilde{t}$ increases, bringing the discontinuity closer to $t_c$. Finally, when $r$ exceeds $r_{c2}$ $\tilde{t}$ coincides with $t_c$ and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.

cond-mat.stat-mech↗

arXiv2015

Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks

We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as $P(k)\sim k^{-λ}$. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case $λ> 5$, reproduces the zeros for the Ising model on a complete graph. For $3<λ< 5$ we derive the $λ$-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the $λ$-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when $3<λ<5$. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee-Yang circle theorem is violated.

cond-mat.stat-mech↗

arXiv2015

Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks

The Ising model on annealed complex networks with degree distribution decaying algebraically as $p(K)\sim K^{-λ}$ has a second-order phase transition at finite temperature if $λ> 3$. In the absence of space dimensionality, $λ$ controls the transition strength; mean-field theory applies for $λ>5$ but critical exponents are $λ$-dependent if $λ< 5$. Here we show that, as for regular lattices, the celebrated Lee-Yang circle theorem is obeyed for the former case. However, unlike on regular lattices where it is independent of dimensionality, the circle theorem fails on complex networks when $λ< 5$. We discuss the importance of this result for both theory and experiments on phase transitions and critical phenomena. We also investigate the finite-size scaling of Lee-Yang zeros in both regimes as well as the multiplicative logarithmic corrections which occur at $λ=5$.

cond-mat.stat-mech↗

arXiv2015

Predicting Results of the Research Excellence Framework using Departmental h-Index -- Revisited

We revisit our recent study [Predicting results of the Research Excellence Framework using departmental h-index, Scientometrics, 2014, 1-16; arXiv:1411.1996] in which we attempted to predict outcomes of the UK's Research Excellence Framework (REF~2014) using the so-called departmental $h$-index. Here we report that our predictions failed to anticipate with any accuracy either overall REF outcomes or movements of individual institutions in the rankings relative to their positions in the previous Research Assessment Exercise (RAE~2008).

cs.DL↗

arXiv2014

On the phase diagram of the 2d Ising model with frustrating dipole interaction

Due to intrinsic frustrations of interaction, the 2d Ising model with competing ferromagnetic short-range nearest-neighbour and antiferromagnetic long-range dipole interactions possesses a rich phase diagram. The order of the phase transition from the striped h=1 phase to the tetragonal phase that is observed in this model has been a subject of recent controversy. We address this question using the partition function density analysis in the complex temperature plane. Our results support the second-order phase transition scenario. To measure the strength of the phase transition we calculate the values of the specific heat critical exponent $α$. Along with the space dimension D, it appears to depend on the ratio of strength of the short-range and long-range interactions.

cond-mat.stat-mech↗

arXiv2013

Phase transitions in the Potts model on complex networks

The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the topology of a network. We consider the q-state Potts model on an uncorrelated scale-free network for which the node-degree distribution manifests a power-law decay governed by the exponent λ. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known to often give asymptotically exact results. Depending on particular values of q and λone observes either a first-order or a second-order phase transition or the system is ordered at any finite temperature. In a case study, we consider the limit q=1 (percolation) and find a correspondence between the magnetic exponents and those describing percolation on a scale-free network. Interestingly, logarithmic corrections to scaling appear at λ=4 in this case.

cond-mat.stat-mech↗

arXiv2013

Comparison of a citation-based indicator and peer review for absolute and specific measures of research-group excellence

Many different measures are used to assess academic research excellence and these are subject to ongoing discussion and debate within the scientometric, university-management and policy-making communities internationally. One topic of continued importance is the extent to which citation-based indicators compare with peer-review-based evaluation. Here we analyse the correlations between values of a particular citation-based impact indicator and peer-review scores in several academic disciplines, from natural to social sciences and humanities. We perform the comparison for research groups rather than for individuals. We make comparisons on two levels. At an absolute level, we compare total impact and overall strength of the group as a whole. At a specific level, we compare academic impact and quality, normalised by the size of the group. We find very high correlations at the former level for some disciplines and poor correlations at the latter level for all disciplines. This means that, although the citation-based scores could help to describe research-group strength, in particular for the so-called hard sciences, they should not be used as a proxy for ranking or comparison of research groups. Moreover, the correlation between peer-evaluated and citation-based scores is weaker for soft sciences.

cs.DL↗

arXiv2012

Marian Smoluchowski: A story behind one photograph

We discuss the photograph procured from the archives of the V. Stefanyk Lviv National Scientific Library of Ukraine dated by 1904 which shows Marian Smoluchowski together with professors and graduate students of the Philosophy department of the Lviv University. The personalia includes both the professors and the graduates depicted on the photograph with the emphasis on the graduates as being much less known and studied. The photograph originates from the collection of the Shevchenko Scientific Society, therefore a brief historical background on the activities of physicists in this society around that period of time is provided as well.

physics.hist-ph↗

arXiv2012

Marginal dimensions for multicritical phase transitions

The field-theoretical model describing multicritical phenomena with two coupled order parameters with n_{||} and n_{\perp} components and of O(n_{||}) \oplus O(n_{\perp}) symmetry is considered. Conditions for realization of different types of multicritical behaviour are studied within the field-theoretical renormalization group approach. Surfaces separating stability regions for certain types of multicritical behaviour in parametric space of order parameter dimensions and space dimension d are calculated using the two-loop renormalization group functions. Series for the order parameter marginal dimensions that control the crossover between different universality classes are extracted up to the fourth order in \varepsilon=4-d and to the fifth order in a pseudo-\varepsilon parameter using the known high-order perturbative expansions for isotropic and cubic models. Special attention is paid to a particular case of O(1) \oplus O(2) symmetric model relevant for description of anisotropic antiferromagnets in an external magnetic field.

cond-mat.stat-mech↗

arXiv2012

Disorder effects on the static scattering function of star branched polymers

We present an analysis of the impact of structural disorder on the static scattering function of f-armed star branched polymers in d dimensions. To this end, we consider the model of a star polymer immersed in a good solvent in the presence of structural defects, correlated at large distances r according to a power law \sim r^{-a}. In particular, we are interested in the ratio g(f) of the radii of gyration of star and linear polymers of the same molecular weight, which is a universal experimentally measurable quantity. We apply a direct polymer renormalization approach and evaluate the results within the double \varepsilon=4-d, δ=4-a-expansion. We find an increase of g(f) with an increasing δ. Therefore, an increase of disorder correlations leads to an increase of the size measure of a star relative to linear polymers of the same molecular weight.

cond-mat.soft↗

arXiv2012

Absolute and specific measures of research group excellence

A desirable goal of scientific management is to introduce, if it exists, a simple and reliable way to measure the scientific excellence of publicly-funded research institutions and universities to serve as a basis for their ranking and financing. While citation-based indicators and metrics are easily accessible, they are far from being universally accepted as way to automate or inform evaluation processes or to replace evaluations based on peer review. Here we consider absolute measurements of research excellence at an amalgamated, institutional level and specific measures of research excellence as performance per head. Using biology research institutions in the UK as a test case, we examine the correlations between peer-review-based and citation-based measures of research excellence on these two scales. We find that citation-based indicators are very highly correlated with peer-evaluated measures of group strength but are poorly correlated with group quality. Thus, and almost paradoxically, our analysis indicates that citation counts could possibly form a basis for deciding on how to fund research institutions but they should not be used as a basis for ranking them in terms of quality.

stat.AP↗

arXiv2012

Fractal transit networks: self-avoiding walks and Lévy flights

Using data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power law behaviour. This indicates that the routes may in part also be described as Lévy-flights. The latter property may result from the fact that the routes are planned to adapt to fluctuating demand densities throughout the served area. We also relate this to optimization properties of Lévy flights.

physics.soc-ph↗

arXiv2012

A tale of two cities. Vulnerabilities of the London and Paris transit networks

This paper analyses the impact of random failure or attack on the public transit networks of London and Paris in a comparative study. In particular we analyze how the dysfunction or removal of sets of stations or links (rails, roads, etc.) affects the connectivity properties within these networks. We show how accumulating dysfunction leads to emergent phenomena that cause the transportation system to break down as a whole. Simulating different directed attack strategies, we find minimal strategies with high impact and identify a-priory criteria that correlate with the resilience of these networks. To demonstrate our approach, we choose the London and Paris public transit networks. Our quantitative analysis is performed in the frames of the complex network theory - a methodological tool that has emerged recently as an interdisciplinary approach joining methods and concepts of the theory of random graphs, percolation, and statistical physics. In conclusion we demonstrate that taking into account cascading effects the network integrity is controlled for both networks by less than 0.5 % of the stations i.e. 19 for Paris and 34 for London.

physics.soc-ph↗

arXiv2012

Shapes of macromolecules in good solvents: field theoretical renormalization group approach

In this paper, we show how the method of field theoretical renormalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on the scaling exponents that govern conformational properties of polymer macromolecules. However, there are other observables that along with the scaling exponents are universal (i.e. independent of the chemical structure of macromolecules and of the solvent) and may be analyzed within the renormalization group approach. Here, we address the question of shape which is acquired by the long flexible polymer macromolecule when it is immersed in a solvent in the presence of a porous environment. This question is of relevance for understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, and in cellular environment. To this end, we consider a previously suggested model of polymers in d-dimensions [V. Blavats'ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) \sim r-a. We apply the field-theoretical renormalization group approach and estimate the size ratio / and the asphericity ratio \hat{A}_d up to the first order of a double ε=4-d, δ=4-a expansion.

cond-mat.soft↗

arXiv2012

Transportation Network Stability: a Case Study of City Traffic

The goals of this paper are to present criteria, that allow to a priori quantify the attack stability of real world correlated networks of finite size and to check how these criteria correspond to analytic results available for infinite uncorrelated networks. As a case study, we consider public transportation networks (PTN) of several major cities of the world. To analyze their resilience against attacks either the network nodes or edges are removed in specific sequences (attack scenarios). During each scenario the size S(c) of the largest remaining network component is observed as function of the removed share c of nodes or edges. To quantify the PTN stability with respect to different attack scenarios we use the area below the curve described by S(c) for c \in [0,1] recently introduced (Schneider, C. M, et al., PNAS 108 (2011) 3838) as a numerical measure of network robustness. This measure captures the network reaction over the whole attack sequence. We present results of the analysis of PTN stability against node and link-targeted attacks.

physics.soc-ph↗

arXiv2011

Analysis of the 3d massive renormalization group perturbative expansions: a delicate case

The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the antiferromagnetic model defined on the stacked triangular lattice. We consider all models at fixed d=3 and analyze the resummation procedures currently used to compute the critical exponents. We first show that, for the O(N) model, the resummation does not eliminate all non-physical (spurious) fixed points (FPs). Then the dependence of spurious as well as of the Wilson-Fisher FPs on the resummation parameters is carefully studied. The critical exponents at the Wilson-Fisher FP show a weak dependence on the resummation parameters. On the contrary, the exponents at the spurious FP as well as its very existence are strongly dependent on these parameters. For the cubic model, a new stable FP is found and its properties depend also strongly on the resummation parameters. It appears to be spurious, as expected. As for the frustrated models, there are two cases depending on the value of the number of spin components. When N is greater than a critical value Nc, the stable FP shows common characteristic with the Wilson-Fisher FP. On the contrary, for N 3, we conclude that the transitions for XY and Heisenberg frustrated magnets are of first order.

cond-mat.stat-mech↗