25 research outputs found
Geometrical properties of Potts model during the coarsening regime
We study the dynamic evolution of geometric structures in a poly-degenerate
system represented by a -state Potts model with non-conserved order
parameter that is quenched from its disordered into its ordered phase. The
numerical results obtained with Monte Carlo simulations show a strong relation
between the statistical properties of hull perimeters in the initial state and
during coarsening: the statistics and morphology of the structures that are
larger than the averaged ones are those of the initial state while the ones of
small structures are determined by the curvature driven dynamic process. We
link the hull properties to the ones of the areas they enclose. We analyze the
linear von-Neumann--Mullins law, both for individual domains and on the
average, concluding that its validity, for the later case, is limited to
domains with number of sides around 6, while presenting stronger violations in
the former case.Comment: 12 page
Classical transverse Ising spin glass with short- range interaction beyond the mean field approximation
The classical transverse field Ising spin- glass model with short-range
interactions is investigated beyond the mean- field approximation for a real d-
dimensional lattice. We use an appropriate nontrivial modification of the
Bethe- Peierls method recently formulated for the Ising spin- glass. The zero-
temperature critical value of the transverse field and the linear
susceptibility in the paramagnetic phase are obtained analytically as functions
of dimensionality d. The phase diagram is also calculated numerically for
different values of d. In the limit d -> infinity, known mean- field results
are consistently reproduced.Comment: LaTex, 11 pages, 2 figure