16 research outputs found
Dynamics of the transverse Ising model with next-nearest-neighbor interactions
We study the effects of next-nearest-neighbor (NNN) interactions on the dynamics of the one-dimensional spin-1/2 transverse Ising model in the high-temperature limit. We use exact diagonalization to obtain the time-dependent transverse correlation function and the corresponding spectral density for a tagged spin. Our results for chains of 13 spins with periodic boundary conditions produce results which are valid in the infinite-size limit. In general we find that the NNN coupling produces slower dynamics accompanied by an enhancement of the central mode behavior. Even in the case of a strong transverse field, if the NNN coupling is sufficiently large, then there is a crossover from collective mode to central mode behavior. We also obtain several recurrants for the continued fraction representation of the relaxation function
Percolation on two- and three-dimensional lattices
In this work we apply a highly efficient Monte Carlo algorithm recently
proposed by Newman and Ziff to treat percolation problems. The site and bond
percolation are studied on a number of lattices in two and three dimensions.
Quite good results for the wrapping probabilities, correlation length critical
exponent and critical concentration are obtained for the square, simple cubic,
HCP and hexagonal lattices by using relatively small systems. We also confirm
the universal aspect of the wrapping probabilities regarding site and bond
dilution.Comment: 15 pages, 6 figures, 3 table
Charging Effects and Quantum Crossover in Granular Superconductors
The effects of the charging energy in the superconducting transition of
granular materials or Josephson junction arrays is investigated using a
pseudospin one model. Within a mean-field renormalization-group approach, we
obtain the phase diagram as a function of temperature and charging energy. In
contrast to early treatments, we find no sign of a reentrant transition in
agreement with more recent studies. A crossover line is identified in the
non-superconducting side of the phase diagram and along which we expect to
observe anomalies in the transport and thermodynamic properties. We also study
a charge ordering phase, which can appear for large nearest neighbor Coulomb
interaction, and show that it leads to first-order transitions at low
temperatures. We argue that, in the presence of charge ordering, a non
monotonic behavior with decreasing temperature is possible with a maximum in
the resistance just before entering the superconducting phase.Comment: 15 pages plus 4 fig. appended, Revtex, INPE/LAS-00
Scaling and universality in the phase diagram of the 2D Blume-Capel model
We review the pertinent features of the phase diagram of the zero-field
Blume-Capel model, focusing on the aspects of transition order, finite-size
scaling and universality. In particular, we employ a range of Monte Carlo
simulation methods to study the 2D spin-1 Blume-Capel model on the square
lattice to investigate the behavior in the vicinity of the first-order and
second-order regimes of the ferromagnet-paramagnet phase boundary,
respectively. To achieve high-precision results, we utilize a combination of
(i) a parallel version of the multicanonical algorithm and (ii) a hybrid
updating scheme combining Metropolis and generalized Wolff cluster moves. These
techniques are combined to study for the first time the correlation length of
the model, using its scaling in the regime of second-order transitions to
illustrate universality through the observed identity of the limiting value of
with the exactly known result for the Ising universality class.Comment: 16 pages, 7 figures, 1 table, submitted to Eur. Phys. J. Special
Topic
Multicritical behavior of the two-dimensional transverse Ising metamagnet in a longitudinal magnetic field
Dynamics of the two-dimensional Heisenberg antiferromagnet in an external magnetic field
In this paper we study the dynamics of the two-dimensional Heisenberg antiferromagnet in an external magnetic field at zero temperature, using the memory function formalism. The imaginary part of the memory function, which is related to the damping, shows a one peak structure. The dynamical structure factor shows a smooth peak well defined separated from another very small peak