9 research outputs found
Stability of a two-sublattice spin-glass model
We study the stability of the replica-symmetric solution of a two-sublattice
infinite-range spin-glass model, which can describe the transition from
antiferromagnetic to spin glass state. The eigenvalues associated with
replica-symmetric perturbations are in general complex. The natural
generalization of the usual stability condition is to require the real part of
these eigenvalues to be positive. The necessary and sufficient conditions for
all the roots of the secular equation to have positive real parts is given by
the Hurwitz criterion. The generalized stability condition allows a consistent
analysis of the phase diagram within the replica-symmetric approximation.Comment: 21 pages, 5 figure
Random-energy model in random fields
The random-energy model is studied in the presence of random fields.
The problem is solved exactly both in the microcanonical ensemble, without
recourse to the replica method, and in the canonical ensemble using the replica
formalism. The phase diagrams for bimodal and Gaussian random fields are
investigated in detail. In contrast to the Gaussian case, the bimodal random
field may lead to a tricritical point and a first-order transition. An
interesting feature of the phase diagram is the possibility of a first-order
transition from paramagnetic to mixed phase.Comment: 18 pages, 5 figures (included
Compressible Sherrington-Kirkpatrick spin-glass model
We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of
elastic degrees of freedom. The problem is formulated in terms of an effective
four-spin Hamiltonian in the pressure ensemble, which can be treated by the
replica method. In the replica-symmetric approximation, we analyze the
pressure-temperature phase diagram, and obtain expressions for the critical
boundaries between the disordered and the ordered (spin-glass and
ferromagnetic) phases. The second-order para-ferromagnetic border ends at a
tricritical point, beyond which the transition becomes discontinuous. We use
these results to make contact with the temperature-concentration phase diagrams
of mixtures of hydrogen-bonded crystals.Comment: 8 pages, 2 figures; added references, added conten
The elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers
We introduce a simple mean-field lattice model to describe the behavior of
nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to
liquid crystals and an extension to lattice systems of the Warner-Terentjev
theory of elasticity, with the addition of quenched random fields. We use
standard techniques of statistical mechanics to obtain analytic solutions for
the full range of parameters. Among other results, we show the existence of a
stress-strain coexistence curve below a freezing temperature, analogous to the
P-V diagram of a simple fluid, with the disorder strength playing the role of
temperature. Below a critical value of disorder, the tie lines in this diagram
resemble the experimental stress-strain plateau, and may be interpreted as
signatures of the characteristic polydomain-monodomain transition. Also, in the
monodomain case, we show that random-fields may soften the first-order
transition between nematic and isotropic phases, provided the samples are
formed in the nematic state.Comment: 17 pages, 7 figure