Abstracts

# Abstracts

**Nerses Ananikian (Yerevan Physics Institute, Alikhanian Br.2, 0036 Yerevan, Armenia). Thermal entanglement & magnetization plateaus of low dimensional spin systems. **Quantum phase transitions play a key role in the understanding the phenomena of many-body systems, especially in antiferromagnetic magnetic plateaus case. Thermal entanglement and magnetization plateaus are detected in spin-1/2 and spin-1 at low dimensional systems. The thermal concurrence and plateaus in Cu-containing compounds are observed on a diamond chain. Thermal negativity as a measure of the quantum entanglement and magnetic plateaus are considered in spin-1 Ni-containing complexes on a diamond chain and polymers.

**Viktor Dotsenko ****(Pierre and Marie Curie University, Paris, France). Recent developments in the KPZ type systems: achievements and attempts that failed .**

In this talk I am going to present a brief review of recent experimental, theoretical and numerical results obtained in the scope of the so called KPZ universality class systems, such as directed polymers in a random potential, time evolution of an interface in disordered media, burning paper profiles, coffee spots, etc.

**Andrzej Jarynowski (Smoluchowski Institute, Jagiellonian University, Cracow, Poland). The influence of temporal aspects and age-correlations on the process of opinion formation based on Polish contact survey.**

On the basis of the experimental data concerning interactions between humans the process of Ising-based model of opinion formation in a social network was investigated. In the paper the data concerning human social activity, i.e. frequency and duration time of interpersonal interactions as well as age correlations - homophily are presented in comparison to base line homogeneous, static and uniform mixing. It is known from previous studies that number of contact and average age of nearest neighbors are highly correlated with age of an individual. Such real, assortative patterns usually speed up processes (like epidemic spread) on the networks, but here it only plays a role for small social temperature values (by reducing `freezing by heating' effect). A real dynamic structure of contacts affects processes in many various studies in different way, however here it causes stronger and smoother susceptibility on external field. Moreover, our research shows that the cross interactions between contact frequency and its duration impose the significant increase in critical temperature.

**Myhajlo Kozlovskii, Oksana Dobush (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine). The state equation of the cell fluid model.**

We propose the method of calculating the grand partition function of multiparticle system, in which constituents interact with each other via potential, that include repulsive and attractive components. The cell model, which was introduced to describe critical phenomena and phase transitions, is used to provide calculations. According to this model, total volume V of a system, is divided into N elementary cells of volume v = V/ N, each of which can host an arbitrary number of particles. Only a form of interaction potential as well as values of its parameters both with a size of elementary cell are required to make computation within this method. The Morse potential is chosen as an interaction potential to provide estimations. We apply an exact procedure of integration over particles coordinates, that makes it possible to obtain an explicit expression for the grand partition function of the fluid cell model in the form of multiple integral over collective variables. As it can be seen directly from the structure of the transition jacobian, the present multiparticle model appeared to be different from the Ising model, which is widely used to describe fluid systems. The state equation, which is valid for wide temperature ranges both above and below the critical one, is derived in zero-order approximation. The pressure calculated for the cell model at temperatures above the critical one is found to be continuously increasing function of temperature and density. Isotherms of pressure as a function of density have horizontal parts at temperatures below the critical one. This fact states about occurance of the first order phase transition in the present model.

**Mariana Krasnytska (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine; Institute Jean Lamour, Groupe de Physique Statistique, Universite de Lorraine, Nancy, France ). Phase transitions on complex networks.**

The critical behavior of several spin models on a scale-free network with a power-law node degree probability distribution and on a complete graph is investigated. The sets of critical exponents, critical amplitude ratios and scaling functions are obtained for the Potts model on a scale-free network by means of the inhomogeneous mean-field approach. The expressions appear to be dependent on the probability distribution function decay exponent.

Applying the method of partition function complex zeros analysis (Lee-Yang-Fisher formalism) we consider the partition function zeros for the Ising model a complete graph and on an annealed scale-free network for complex temperature (Fisher zeros) or for complex magnetic field (Lee-Yang zeros). The characteristics describing zeros location are found. In case of an annealed scale-free network they depend on the node degree distribution function decay. It is known that Lee-Yang zeros of the ferromagnetic Ising model on a lattice satisfy the unit circle Lee-Yang theorem: all zeros are imaginary in the complex magnetic field plane. We prove that this theorem does not hold for the Ising model on annealed scale-free network: there appear zeros with both, real and imaginary, parts and the Lee-Yang circle theorem is violated.

This talk gives a short account of a PhD thesis prepared in the frames of the Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L4).

**Olesya Mryglod (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine ). Quantifying scientific impact: networks, measures, insights?**

While peer review and citations reflect opinion about a paper's quality and scientific impact after reading, downloads rather reflect interest before reading. In other words, in addition to popularity and prestige, papers may be distinguished by their attractiveness. In such a classification, the overall number of citations measures popularity, the number of important citations is evidence of prestige, whereas the number of downloads reflects the level of attractiveness of a publication.

In our work the downloading statistics of publications in «Europhysics Letters» journal is analysed. We find that the journal is characterised by fast accumulation of downloads during the first couple of months after publication, followed by a slower rate thereafter. This behaviour can be modelled, so that the long-time download patterns for the journal can be predicted. We also find that individual papers can be classified in various ways according to their downloading statistics.

**Thierry Platini (Applied Mathematics Research Centre, Coventry University, UK). Analytical results for stochastic gene expression models.**

Gene expression (GE) is the set of bio mechanism by which information from a gene is used to synthesize RNA macromolecules and proteins. Cells have at their disposal different biological processes to regulate protein level and noise. One challenge of particular interest is the understanding of the mechanisms leading to phenotypic heterogeneity amongst genetically identical cells. Obtaining exact analytical results for protein and mRNA distributions is a challenging task for all but the simplest models of GE. The partitioning property of Poisson processes allows to develop a mapping reducing creation/degradation mechanisms to simple biological switches. This mapping provides a new way to tackle some of the favourite models of GE. Using this approach, we derive exact analytical results for time-dependent distributions of the variations of basic two-stage model.

**Petro Sarkanych (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine; ****Applied Mathematics Research Centre, Coventry University, UK****).** 1D Potts model with invisible states.

We present an exact solution of the 1D Potts model with invisible states. The model was introduced a few years ago to explain some untypical phase transitions with spontaneous symmetry breaking. In addition to ordinary Potts states this model possesses states which do not interact, and thus contribute to the entropy, but not to the interaction energy. The number of invisible states plays a role of a parameter, which changes the order of a phase transition.

Using transfer matrix method we obtain the partition function of the model at the presence of two ordering fields, acting on the first visible and on the first invisible states, correspondingly. We further analyse partition function zeros in complex temperatute and complex magnetic field planes (Fisher and Lee-Yang zeros) and discuss resulting critical behaviour.

This work is a part of a PhD thesis under preparation in the frames of the Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L4).