Issue 2

JTAM, Sofia, vol. 51 Issue 2 (2021)

In memory of JORDAN G. BRANKOV

N.S. Tonchev
Guest Editor


This issue is devoted to the memory of Professor Jordan Georgiev Brankov, or Dancho for his friends and colleagues, a well-known Bulgarian theoretical physicist.

By the presented collection of papers, his colleagues, co-authors and friends pay their tribute to his memory and acknowledge his recognized contribution to statistical mechanics and condensed matter physics. The articles are in various fields, thus reflecting the topics Dancho had close interests in, and worked over the years.

JTAM, Sofia, vol. 51 Issue 2 pp. 105-107 (2021), [Full Article]


SCALING BEHAVIOR OF CONFINED O(n) SYSTEMS INVOLVING LONG-RANGE INTERACTION

H. Chamati
Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko Chaussée 72, 1784 Sofia, Bulgaria

To explore the finite-size scaling in confined systems involving an interaction with long-range tail one needs the development of suitable mathematical techniques. In the present review we consider the scaling behavior of the finite O(n) model with long-range interaction that is widely used in the theory of classical and quantum phase transitions. We consider finite geometries subject to periodic boundary conditions. The present mathematical method may be used to compute different thermodynamic quantities such as: the free energy, the susceptibility, specific heat etc. Here, we present results for the susceptibility in different regions of the phase diagram. Furthermore, we investigate the effect of classical and quantum fluctuations and check various scaling hypotheses.

JTAM, Sofia, vol. 51 Issue 2 pp. 108-122 (2021), [Full Article]


ON DYNAMICS OF AN OPEN BOSON SYSTEM

Valentin A. Zagrebnov
Institut de Mathématiques de Marseille CMI - AMU Technopôle Château-Gombert, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France

The core property of generator and the trace-preserving property of a minimal dynamical semigroup constructed by regularisation á la Kato are scrutinised for a simple boson model in the framework of the Gorini–Kossakowski–Lindblad–Davies approach to the open systems.

JTAM, Sofia, vol. 51 Issue 2 pp. 123-153 (2021), [Full Article]


ON THE RELATION BETWEEN THE MONOTONE RIEMANNIAN METRICS ON THE SPACE OF GIBBS THERMAL STATES AND THE LINEAR RESPONSE THEORY

N.S. Tonchev
Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko Chaussée 72, 1784 Sofia, Bulgaria

The proposed in J. Math. Phys. v.57, 071903 (2016) analytical expansion of monotone (contractive) Riemannian metrics (called also quantum Fisher information(s)) in terms of moments of the dynamical structure factor (DSF) relative to an original intensive observable is reconsidered and extended. The new approach through the DSF which characterizes fully the set of monotone Riemannian metrics on the space of Gibbs thermal states is utilized to obtain an extension of the spectral presentation obtained for the Bogoliubov–Kubo–Mori metric (the generalized isothermal susceptibility) on the entire class of monotone Riemannian metrics. The obtained spectral presentation is the main point of our consideration. The last allows to present the one to one correspondence between monotone Riemannian metrics and operator monotone functions (which is a statement of the Petz theorem in the quantum information theory) in terms of the linear response theory. We show that monotone Riemannian metrics can be determined from the analysis of the infinite chain of equations of motion of the retarded Green’s functions. Inequalities between the different metrics have been obtained as well. It is a demonstration that the analysis of information-theoretic problems has benefited from concepts of statistical mechanics and might cross-fertilize or extend both directions, and vice versa. We illustrate the presented approach on the calculation of the entire class of monotone (contractive) Riemannian metrics on the examples of some simple but instructive systems employed in various physical problems.

JTAM, Sofia, vol. 51 Issue 2 pp. 154-186 (2021), [Full Article]


ON THE FINITE-SIZE BEHAVIOR OF ONE BASIC MODEL OF STATISTICAL MECHANICS DESCRIBING SECOND ORDER PHASE TRANSITION

D. Dantchev1,2,3
1Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev St., Block 4, 1113 Sofia, Bulgaria
2Max-Planck-Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart, Germany
3Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

We present a short review and some new results on the finite-size behavior of finite systems exhibiting second order phase transition. We will be mainly focused on one basic model of statistical mechanics — the Ginzburg–Landau ϕ4 model under the influence of temperature bath and an external ordering field.

JTAM, Sofia, vol. 51 Issue 2 pp. 187-202 (2021), [Full Article]


LAMELLAR-TO-INVERTED HEXAGONAL PHASE TRANSITION IN LYOTROPIC LIQUID CRYSTALS IN THE PRESENCE OF HOFMEISTER SOLUTES

Rumiana Koynova1, Boris Tenchov2,3
1Ohio State University College of Pharmacy, Columbus, OH 43210, USA
2Laboratory of Medical Nanotechnologies, Dept. Medical Physics and Biophysics, Medical University-Sofia, 1431 Sofia, Bulgaria
3Bulgarian Academy of Sciences, 1040 Sofia, Bulgaria

The Hofmeister effect refers to the effects of ions and small non-ionic solutes, termed Hofmeister solutes, on a wide range of phenomena in aqueous milieu, such as colloid stability, critical micelle concentration, emulsion microstructure, cloud points of polymer solutions, zeta potentials, ion binding to interfaces, phase transitions in lipid dispersions and many other. Using an equation of Clapeyron-Clausius type, derived by our late colleague Professor Jordan G. Brankov in our previous study on the Hofmeister effect (European Biophysics Journal (1997) 25 261-274), here we analyze the relation of the lipid headgroup hydration to the effect of Hofmeister solutes on the lamellar-to-inverted hexagonal phase transition in aqueous lipid dispersions and develop a new approach for determination of the headgroup hydration difference between the lamellar and inverted hexagonal phases.

JTAM, Sofia, vol. 51 Issue 2 pp. 203-217 (2021), [Full Article]


HIGH-TEMPERATURE EXPANSIONS FOR THE SPIN = 1 HEISENBERG MODEL: THE CASE OF THE HEXAGONAL FERRIMAGNET RbNiF3

Kiril A. Krezhov
Institute for Nuclear Research and Nuclear Energy and Institute of Electronics, Bulgarian Academy of Sciences, Tsarigradsko Chaussée 72, 1784 Sofia, Bulgaria

The high-temperature series in powers of reciprocal temperature up to sixth order for the magnetic susceptibility χ and up to fifth order for specific heat were determined for a three dimensional Heisenberg model of a hexagonal ferrimagnet with competing interactions (two different of opposite signs first neighbour exchange constants) and any spin value S. The scheme of spin-spin interactions is open, in the sense that the neighbors to whom a given site is coupled do not interact with each other. The power series were analysed by the method of optimal transformation of the variable. The study was carried out for the ratio of exchange constants R = J2/J1 in the interval -3.0 < R < -0.2 (J1 < 0, J2 > 0). The behaviour of the magnetic susceptibility and specific heat by taking into account the dominant coupling constants and the spin number S = 1 valid for RbNiF3 is presented and compared with available theoretical and experimental results.

JTAM, Sofia, vol. 51 Issue 2 pp. 218-241 (2021), [Full Article]


TASEP ON NETWORKS WITH NONTRIVIAL GEOMETRY CONSISTING OF COUPLED SIMPLE LINEAR CHAINS

Nadezhda Bunzarova, Nina Pesheva
Instititute of Mechanics, Bulgarian Academy of Sciences

We briefly overview some of our recent advances in the study of non-equilibrium phenomena with emphasis on steady state properties of the totally asymmetric simple-exclusion process (TASEP) defined on an open network containing a double-chain section in the bulk (i.e., a network, having a bifurcation and merging points). We consider different possible scenarios for the specific realizations of the network falling in two basic cases — the double-chain section consisting of chains with equal or different lengths. We refer to the latter case as a shortcut in the bulk. The phase compositions of these types of networks, depending on the rates of input and output of particles at the open ends, the conditions for occurrence of traffic jams and their properties, were determined by using both theoretical and numerical methods. We concisely present the simple theory of Effective Rates Approximation by the help of which, ignoring the correlations at the junctions of the chain segments, the possible phase structures of the network models are found.

JTAM, Sofia, vol. 51 Issue 2 pp. 242-273 (2021), [Full Article]