STATISTICAL PHYSICS: MODERN TRENDS AND APPLICATIONS: The 3rd Conference on Statistical Physics Dedicated to the 100th Anniversary of Mykola Bogolyubov

Network harness: bundles of routes in public transport networks
View Description Hide DescriptionPublic transport routes sharing the same grid of streets and tracks are often found to proceed in parallel along shorter or longer sequences of stations. Similar phenomena are observed in other networks built with space consuming links such as cables, vessels, pipes, neurons, etc. In the case of public transport networks (PTNs) this behavior may be easily worked out on the basis of sequences of stations serviced by each route. To quantify this behavior we use the recently introduced notion of network harness. It is described by the harness distribution P(r, s): the number of sequences of s consecutive stations that are serviced by r parallel routes. For certain PTNs that we have analyzed we observe that the harness distribution may be described by power laws. These power laws indicate a certain level of organization and planning which may be driven by the need to minimize the costs of infrastructure and secondly by the fact that points of interest tend to be clustered in certain locations of a city. This effect may be seen as a result of the strong interdependence of the evolutions of both the city and its PTN.
To further investigate the significance of the empirical results we have studied one‐ and two‐dimensional models of randomly placed routes modeled by different types of walks. While in one dimension an analytic treatment was successful, the two dimensional case was studied by simulations showing that the empirical results for real PTNs deviate significantly from those expected for randomly placed routes.

Mesoscopic theory for soft‐matter systems
View Description Hide DescriptionA mesoscopic description of various systems containing spherical charged particles in solvent inducing effective attraction is developed by a systematic coarse‐graining procedure. For weak ordering the theory can be reduced to the Landau‐Ginzburg or the Landau‐Brazovskii field theory, depending on the form of the effective interactions between particles. Within the framework of this theory we obtain and discuss the λ‐line and the universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close‐packing density. The sequence of phases agrees with experimental observations and with simulations of many self‐assembling systems. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short‐range attraction long‐range repulsion potential we find the bicontinuous gyroid phase (Ia3d symmetry) that may be related to a network forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.

The kinetic regime of the Vicsek model
View Description Hide DescriptionWe consider the dynamics of the system of self‐propelling particles modeled via the Vicsek algorithm in continuum time limit. It is shown that the alignment process for the velocities can be subdivided into two regimes: “fast” kinetic and “slow” hydrodynamic ones. In fast kinetic regime the alignment of the particle velocity to the local neighborhood takes place with characteristic relaxation time. So, that the bigger regions arise with the velocity alignment. These regions align their velocities thus giving rise to hydrodynamic regime of the dynamics. We propose the mean‐field‐like approach in which we take into account the correlations between density and velocity. The comparison of the theoretical predictions with the numerical simulations is given. The relation between Vicsek model in the zero velocity limit and the Kuramoto model is stated. The mean‐field approach accounting for the dynamic change of the neighborhood is proposed. The nature of the discontinuity of the dependence of the order parameter in case of vectorial noise revealed in Gregorie and Chaite, Phys. Rev. Lett., 92, 025702 (2004) is discussed and the explanation of it is proposed.

Superfluid state of magnetoexcitons in double layer graphene structures
View Description Hide DescriptionThe possibility of realizing a superfluid state of bound electron‐hole pairs (magnetoexcitons) with spatially separated components in a graphene double layer structure (two graphene layers separated by a dielectric layer) subjected to a strong perpendicular to the layers magnetic field is analyzed. We show that the superfluid state of magnetoexcitons may emerge only under certain imbalance of filling factors of the layers. The imbalance can be created by an electrostatic field (external gate voltage). The spectrum of elementary excitations is found and the dependence of the Berezinskii‐Kosterlitz‐Thouless transition temperature on the interlayer distance is obtained. The advantages of using the graphene double layer systems instead of double quantum well GaAs heterostructures are discussed.

The quenched‐disordered Ising model in two and four dimensions
View Description Hide DescriptionWe briefly review the Ising model with uncorrelated, quenched random‐site or random‐bond disorder, which has been controversial in both two and four dimensions. In these dimensions, the leading exponent α, which characterizes the specific‐heat critical behaviour, vanishes and no Harris prediction for the consequences of quenched disorder can be made. In the two‐dimensional case, the controversy is between the strong universality hypothesis which maintains that the leading critical exponents are the same as in the pure case and the weak universality hypothesis, which favours dilution‐dependent leading critical exponents. Here the random‐site version of the model is subject to a finite‐size scaling analysis, paying special attention to the implications for multiplicative logarithmic corrections. The analysis is fully supportive of the scaling relations for logarithmic corrections and of the strong scaling hypothesis in the 2D case. In the four‐dimensional case unusual corrections to scaling characterize the model, and the precise nature of these corrections has been debated. Progress made in determining the correct 4D scenario is outlined.

A simple approach to magnetoelectric correlations in ferroelectric ferromagnets: the case of
View Description Hide DescriptionWe discuss a simple version of Landau theory with two single‐component order parameters, P and M, corresponding to the ferroelectric and ferromagnetic phases coupled to each other via a term. In the case of ferroelectricity appearing at a temperature much higher than that of a ferromagnetic transition, the latter is strongly renormalized ( ). The thermodynamics of the model in spatially homogeneous phases is elaborated first. Our simple formulation is applied next to and provides a good semiquantitative description of the magnetic and dielectric properties except for the specific heat, which is not entirely explained in the regime even when the Gaussian fluctuations of the order parameters are included. Possible improvements to our approach are briefly discussed.

Some semi‐phenomenological approaches to description of microcrack formation in solids
View Description Hide DescriptionSome semi‐phenomenological models of crack formation in solids under homogenous stress field are considered. It is shown that microcracks (MCRs) of typical lengths are being healed due to thermally activated surface diffusion processes, while at the length at which a maximum of the total energy of the MCR occurs, there is an instantaneous material destruction. We also consider the penetration of a guest‐particle inside the defect. Mutual repulsion between host‐and guest‐particles creates stable defects in the solid. Stability of such MCRs with respect to temperature fluctuations grows in a certain range of strains and then decreases. The formation of a bridge between host‐ and guest‐particles extends this region and enhances the stability of microdefects.

High‐frequency impedance of layered conductors in a quantizing magnetic field
View Description Hide DescriptionPropagation of electromagnetic waves in layered conductors placed in a strong magnetic field is studied theoretically. Quantum oscillations of the impedance of a conductor are calculated for a wide range of electromagnetic wave frequencies.

Semi‐infinite metal: thermodynamic potential and effective interionic pair potentials
View Description Hide DescriptionA general expression for thermodynamic potential of semi‐infinite metal is obtained. This expression has the form of expansion in powers of pseudo‐potential degrees. It is shown, that multi‐particle effective interionic potentials are necessary for calculation of the thermodynamic potential. The detailed analysis of interionic pair potential is made. The effect of geometrical limitation of metal on the behaviour of this potential is investigated.

Equilibrium dynamics and phase transitions in quantum anharmonic crystals
View Description Hide DescriptionFor a system of interacting quantum anharmonic (double‐welled) oscillators (quantum anharmonic crystal), it is shown that a phase transition can cause the equilibrium dynamics of a given oscillator to be reducible. This means that the oscillator prefers one of the wells. Sufficient conditions for this effect to occur at some temperature, or not to occur at all temperatures, are presented.

Phase transitions in Ising Chains?
View Description Hide DescriptionAn open question in the study of the spin‐1/2 Ising model is the solution of the two‐dimensional case in the presence of a magnetic field. A possible answer is based on the study of L‐coupled linear chains in the limit of large L. Results reported in the literature show that a dimensional crossover from the one to the two dimensional model does not exist. However, what happens if one considers open boundary conditions (BC)? In this article I show that, for an appropriate choice of the BC, a system of L‐chains exhibits a ferromagnetic order characterized by a critical temperature which, for zero magnetic field, tends to the Onsager’s one as L increases. It is then possible to study the phase diagram in the (h, T) plane and obtain a solution for finite magnetic field.

Transverse dynamics of a quasi‐ideal binary fluid: mass asymmetry effects
View Description Hide DescriptionThe effect of mass asymmetry on the transverse dynamics of the binary symmetric mixture is investigated by combining the molecular dynamic (MD) simulations and parameter‐free generalized collective mode (GCM) approach. The dependence of shear viscosity on the mass ratio of particles in the species is represented. A good agreement between results obtained using Green‐Kubo formula and relation for correlation time of total momentum correlation function is found in a wide range of mass asymmetry. The behaviour of two lowest lying propagating modes is studied analytically within the four‐variable approximation of GCM approach. It is established that if the mass ratio increases the propagating gap for shear waves becomes wider. However, if the concentration of heavy particles increases an opposite tendency is observed. The time correlation functions (TCFs) are calculated within this simplified four‐variable scheme and a good agreement with results of direct MD simulations for these quantities is found.

Exact results for the solvation force in 2D Ising stripes
View Description Hide DescriptionThe solvation force for two‐dimensional Ising stripes in the presence of boundary fields is calculated via exact diagonalization of the transfer matrix in two cases: the symmetric case corresponds to identical boundary fields and the antisymmetric case to exactly opposite boundary fields. In the symmetric case the solvation force is always negative (attractive), while in the antisymmetric case it is positive (repulsive) at high temperatures and negative at low temperatures. It changes sign close to the critical wetting temperature characterizing the semi‐infinite system. The properties of the solvation force are discussed, and the scaling function describing its dependence on temperature, boundary field, and stripe’s width is proposed.

Gas‐liquid critical point in model ionic fluids with charge and size asymmetry
View Description Hide DescriptionWe study the effects of size and charge asymmetry on the gas‐liquid critical parameters of a primitive model (PM) of ionic fluids. The model is characterized by the two parameters: hard‐sphere diameter‐, and charge, ratios of the two ionic species. Using the collective variables based theory we calculate the critical temperature and the critical density for the two versions of PM: an equisize PM with charge asymmetry ( , and a monovalent PM with size asymmetry ( ). The trends obtained for the both critical parameters of the models under consideration agree qualitatively with Monte Carlo simulation findings.

Calculation of free energy of three‐dimensional uniaxial magnet in external field based on the higher non‐Gaussian distribution
View Description Hide DescriptionThe analytical calculation of the free energy of a three‐dimensional Ising‐like system in a homogeneous external field is performed in the higher non‐Gaussian approximation (the model) at temperatures above the critical value of ( is the phase‐transition temperature in the absence of an external field). The free energy of the system is found by separating the contributions from the short‐ and long‐wave spin‐density oscillation modes taking into account the generalized point of exit of the system from the critical regime as a function of both the temperature and field variables. A calculation technique is based on the first principles of statistical physics and is naturally realized without any general assumptions and without any adjustable parameters. The obtained expression for the free energy does not involve series expansions in the scaling variable and is valid near the critical point not only in the regions of the so‐called weak and strong external fields but also in the crossover region between these fields. In this region, the temperature and field effects on the system are equivalent, the scaling variable is of the order of unity and power series are not efficient. The free energy contains the leading terms and terms determining the temperature and field confluent corrections.

Massive field theory approach for polymer chains in confined geometries
View Description Hide DescriptionUsing the massive field theory approach directly at fixed dimensions we calculated the depletion interaction potential and the depletion force between two repulsive, two inert and one repulsive and one inert wall confining a dilute solution of long flexible polymer chains. The obtained calculations for all cases of polymer‐surface interactions were performed for an ideal chain and a real polymer chain with excluded volume interactions (EVI) in the wide slit regime. Besides, we used some assumptions which allowed us to estimate the depletion interaction potential in the region of narrow slit. The obtained results are in very good agreement with previous theoretical investigations and with the results of Monte Carlo simulations for the case of two repulsive walls. Taking into account the Derjaguin approximation we obtained good qualitative agreement with the experimental data for the depletion potential between a spherical colloidal particle of big radius and repulsive wall. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with EVI than for ideal chains, because the EVI effectively reduces the depletion effect near the walls.

Weak‐universal critical behavior and quantum critical point of the exactly soluble spin‐1/2 Ising‐Heisenberg model with the pair XYZ Heisenberg and quartic Ising interactions
View Description Hide DescriptionSpin‐1/2 Ising‐Heisenberg model withXYZ Heisenberg pair interaction and two different Ising quartic interactions is exactly solved with the help of the generalized star‐square transformation, which establishes a precise mapping equivalence with the corresponding eight‐vertex model on a square lattice generally satisfying Baxter’s zero‐field (symmetric) condition. The investigated model exhibits a remarkable weak‐universal critical behavior with two marked wings of critical lines along which critical exponents vary continuously with the interaction parameters. Both wings of critical lines merge together at a very special quantum critical point of the infinite order, which can be characterized through diverging critical exponents. The possibility of observing reentrant phase transitions in a close vicinity of the quantum critical point is related to a relative strength of the exchange anisotropy in the XYZ Heisenberg pair interaction.

Self‐organization processes at exciton condensation in quantum wells
View Description Hide DescriptionThe problem of phase transitions in a system of particles with finite value of the lifetime is analyzed. As an example the theory of condensation of indirect excitons in semiconductor double quantum wells is presented. For description of a spatial distribution of condensed and gas phases two models of phase transitions are used: the model of nucleation and growth and the model of spinodal decomposition generalized on unstable particles. It is shown that due to finite value of the exciton lifetime the sizes of condensed phases are restricted and in two‐dimensional case, the regions of condensed phase have the shape of islands located within the excitonic gas. There is specific interaction between islands of the condensed phase through exciton concentration fields. This interaction causes the development of different structures of exciton condensed phases in the crystal irradiated by light. The evolution of the islands of condensed phase is studied depending on the changes of the temperature, pumping and the presence of external potential.

The theory of electro‐magnetic radiation of electron transiting through the resonance‐tunnel structure
View Description Hide DescriptionThe quasi‐stationary electron states are studied in the three‐barrier resonance‐tunnel structure which is the basic element of coherent quantum cascade lasers. In the models of rectangular and δ‐barrier potentials there is established theory of evolution and collapse of double resonance complexes in a symmetric resonance‐tunnel structure. The induced conductivity of nano‐system is calculated within the both models. It is shown that the negative induced conductivity of three‐barrier resonance‐tunnel structure in δ‐barrier model is dozens times smaller than more realistic magnitudes obtained within the rectangular potentials model.