34,427 research outputs found
No spin glass phase in ferromagnetic random-field random-temperature scalar Ginzburg-Landau model
Krzakala, Ricci-Tersenghi and Zdeborova have shown recently that the random
field Ising model with non-negative interactions and arbitrary external
magnetic field on an arbitrary lattice does not have a static spin glass phase.
In this paper we generalize the proof to a soft scalar spin version of the
Ising model: the Ginzburg-Landau model with random magnetic field and random
temperature-parameter. We do so by proving that the spin glass susceptibility
cannot diverge unless the ferromagnetic susceptibility does.Comment: 9 page
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
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