International Journal of Modern Physics B

The statistical mechanics of fluctuating surfaces plays an important role in a variety of physical systems, ranging from biological membranes to world sheets of strings in theories of fundamental interactions. In many applications it is a good approximation to assume that the surfaces possess no tension. Their statistical properties are then governed by curvature energies only, which allow for gigantic out-of-plane undulations. These fluctuations are the “entropic” origin of long-range repulsive forces in layered surface systems. Theoretical estimates of these forces for simple model surfaces are surveyed and compared with recent Monte Carlo simulations.

The modern state of the theory of topological constraints in statistical physics of polymers is reviewed. Attention is paid mainly to the most general problems concerning the topological properties of polymers represented as Markov paths. The different approaches and methods used for solving the concrete topological problems are systematized. On the phenomenological level the role of topological constraints in kinetics of polymers is investigated.

The macroscopical Ginzburg-Landau models with effective-mass tensor and Josephson coupling of the layers are used to describe the magnetic properties of layered superconductors (dichalcogenides of transition metals and intercalated compounds, organic superconductors and high-T_c copper oxide compounds). In the framework of such models the magnetic critical fields, Abrikosov lattice, torque, Josephson oscillations, Gaussian fluctuations are considered and the validity of mean field theory in the model with Josephson coupling is discussed. The layeredcompounds with different superconducting layers are also studied including the dependence of critical temperature on the strength of coupling and temperature dependence of magnetic anisotropy. The experimental data of high-T_c superconductors are discussed to show that in Bi- and Tl-compounds the conditions of Josephson coupling of layers is fulfilled.

The formation and stability of the Fröhlich bipolaron in a multi-dimensional polar crystal is investigated within the framework of strong coupling Landau-Pekar theory. The ground state energy, the effective mass and the size of the bipolaron are calculated. It is shown that Fröhlich bipolarons can exist in both two and three dimensions, the bipolaronic binding being stronger in lower dimensions. The dimensional scaling relations satisfied by the ground state energy and the effective mass of the bipolaron are also obtained.

Infrared reflectance of GdBa₂Cu(1−x)₃Ag_3xO₇ ceramic superconductor with the composition of x=0.025 and 0.05 have been performed in the frequency range of 100–5000 cm⁻¹. All the infrared active phonon modes allowed by the selection rules were observed in the reflection spectra of these compounds. The optical conductivity as calculated from K-K analysis further confirms the existence of these optical phonons. Besides the increase of the reflectivity in the silver doped samples, an extra phonon mode is observed, which is normally not seen at room temperature reflectance of GdBa₂Cu₃O₇ compounds. The four probe resistivity measurement show zero resistance at 88 K for x=0, and 78 K for x=0.025 in GdBa₂Cu(1−x)₃Ag_3xO₇ compound.

We describe new local relations leading to non-trivial (non-homogeneous) equations for the row-to-row transfer matrices of arbitrary size for two dimensional I.R.F. and vertex models. We sketch the connection between this relation and the Yang-Baxter equations, and we describe the example of the hard hexagon model.

We give in explicit form a very general relation between the solution of the spherical model on a graph and the statistics of walks on the same graph. Such formulation sheds light on the role of topology in the statistical behaviour of model systems, since a graph is meant as a geometrical entity with no regard to any embedding space. This includes, of course, euclidean and fractal lattices as in particular cases. In this work we also show how this relation can be exploited to actually compute the thermodynamics of the model on a class of infinite graphs by giving the exact solution on Bethe lattices, where no euclidean metrics can be defined.