Spectral Properties of the Generalized Spin-Fermion Models

In order to account for competition and interplay of localized and itinerant magnetic behaviour in correlated many body systems with complex spectra the various types of spin-fermion models have been considered in the context of the Irreducible Green's Functions (IGF) approach. Examples are generalized d-f model and Kondo-Heisenberg model. The calculations of the quasiparticle excitation spectra with damping for these models has been performed in the framework of the equation- of-motion method for two-time temperature Green's Functions within a non-perturbative approach. A unified scheme for the construction of Generalized Mean Fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation has been generalized in order to include the presence of the two interacting subsystems of localized spins and itinerant electrons. A general procedure is given to obtain the quasiparticle damping in a self-consistent way. This approach gives the complete and compact description of quasiparticles and show the flexibility and richness of the generalized spin-fermion model concept.Comment: 37 pages, Late

Unconventional and Exotic Magnetism in Carbon-Based Structures and Related Materials

The detailed analysis of the problem of possible magnetic behavior of the carbon-based structures was fulfilled to elucidate and resolve (at least partially) some unclear issues. It was the purpose of the present paper to look somewhat more critically into some conjectures which have been made and to the peculiar and contradictory experimental results in this rather indistinct and disputable field. Firstly the basic physics of magnetism was briefly addressed. Then a few basic questions were thoroughly analyzed and critically reconsidered to elucidate the possible relevant mechanism (if any) which may be responsible for observed peculiarities of the "magnetic" behavior in these systems. The arguments supporting the existence of the intrinsic magnetism in carbon-based materials, including pure graphene were analyzed critically. It was concluded that recently published works have shown clearly that the results of the previous studies, where the "ferromagnetism" was detected in pure graphene, were incorrect. Rather, graphene is strongly diamagnetic, similar to graphite. Thus the possible traces of a quasi-magnetic behavior which some authors observed in their samples may be attributed rather to induced magnetism due to the impurities, defects, etc. On the basis of the present analysis the conclusion was made that the thorough and detailed experimental studies of these problems only may shed light on the very complicated problem of the magnetism of carbon-based materials. Lastly the peculiarities of the magnetic behavior of some related materials and the trends for future developments were mentioned.Comment: 40 pages, 5 tables, 221 Reference

Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of N. N. Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics and condensed matter physics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach, and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem, in which the effect of all the other particles on any given particle is approximated by a single averaged effect, thus reducing a many-body problem to a single-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising and Heisenberg models, superconducting and superfluid systems, strongly correlated systems, etc. It seems likely that these technical advances in the many-body problem will be useful in suggesting new methods for treating and understanding many-particle interacting systems. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects, and for those who are interested in concrete applications.Comment: 60 pages, Refs.25