Statistical mechanics of high-density bond percolation

High-density (HD) percolation describes the percolation over specific $\kappa$ -clusters, which are the compact sets of sites each connected to $\kappa$ nearest filled sites at least. It takes place in the classical patterns of independently distributed sites or bonds in which the ordinary percolation transition also exsists. Hence, the study of series of $\kappa$ -type percolations amounts to the description of structure of classical clusters for which $\kappa$ -clusters constitute $\kappa$ -cores nested one into another. Such data are needed for description of a number of physical, biological information and other properties of complex systems on random lattices, graphs and networks. They range from magnetic properties of semiconductor alloys to anomalies in supercooled water and clustering in biological and social networks. Here we present the statistical mechanics approach to study HD bond percolation on arbitrary graph. It is shown that generating function for $\kappa$ -clusters' size distribution can be obtained from partition function of specific $q$-state Potts-Ising model in $q \to 1$ limit. Using this approach we find exact $\kappa$ -clusters' size distribution for Bethe lattice and Erdos Renyi graph. The application of the method to Euclidean lattices is also discussed.Comment: 12 pages, 1 figur

Dipole-glass concept and history-dependent phenomena in relaxors

The possibility to explain basic physical properties of relaxors within the concept of the dipole-glass transition is discussed. We argue that this concept provides the only consistent picture accounting of all known anomalous features of relaxors. The origin of their history-dependent properties can be naturally traced to the main paradigm of glass-state theory - the existence of numerous metastable states. Based on this paradigm phenomenological description of known history-dependent phenomena in relaxors agrees qualitatively with experiments.Comment: 9 pages, 6 figure

Phenomenological theory of nonergodic phenomena in dipole- and spin-glasses

The path-dependent magnetizations (polarizations) and susceptibilities in dipole- and spin-glasses are described analytically for the standard protocols of temperature and field variations using the phenomenological Landau-type description of multiple metastable states in the nonergodic phases. The immediate manifestation of metastable states' multiplicity as staircases of magnetizations (polarizations) curves in the temperature cycling experiments is explained and described. The obtained results are in a reasonable qualitative agreement with the existing experimental data.Comment: 12 pages, 9 figure

Phase transitions in random magnetic bilayer

The influence of random interlayer exchange on the phase states of the simplest magnetic heterostructure consisting of two ferromagnetic Ising layers with large interaction radius is studied. It is shown that such system can exist in three magnetic phases: ferromagnetic, antiferromagnetic and ferrimagnetic. The possible phase diagrams and temperature dependencies of thermodynamic parameters are described. The regions of existence of the magnetic phases in external magnetic field are determined at zero temperature.Comment: 6 pages, 4 figures; typos corrected, explanation of mechanism underlying the appearance of ferrimagnetic states adde