34 research outputs found
Equilibrium crystal shapes in the Potts model
The three-dimensional -state Potts model, forced into coexistence by
fixing the density of one state, is studied for , 3, 4, and 6. As a
function of temperature and number of states, we studied the resulting
equilibrium droplet shapes. A theoretical discussion is given of the interface
properties at large values of . We found a roughening transition for each of
the numbers of states we studied, at temperatures that decrease with increasing
, but increase when measured as a fraction of the melting temperature. We
also found equilibrium shapes closely approaching a sphere near the melting
point, even though the three-dimensional Potts model with three or more states
does not have a phase transition with a diverging length scale at the melting
point.Comment: 6 pages, 3 figures, submitted to PR
Properties of Interfaces in the two and three dimensional Ising Model
To investigate order-order interfaces, we perform multimagnetical Monte Carlo
simulations of the and Ising model. Following Binder we extract the
interfacial free energy from the infinite volume limit of the magnetic
probability density. Stringent tests of the numerical methods are performed by
reproducing with high precision exact results. In the physically more
interesting case we estimate the amplitude of the critical
interfacial tension to be . This
result is in good agreement with a previous MC calculation by Mon, as well as
with experimental results for related amplitude ratios. In addition, we study
in some details the shape of the magnetic probability density for temperatures
below the Curie point.Comment: 25 pages; sorry no figures include
Monte Carlo Renormalization Group Analysis of Lattice Model in
We present a simple, sophisticated method to capture renormalization group
flow in Monte Carlo simulation, which provides important information of
critical phenomena. We applied the method to lattice model and
obtained renormalization flow diagram which well reproduces theoretically
predicted behavior of continuum model. We also show that the method
can be easily applied to much more complicated models, such as frustrated spin
models.Comment: 13 pages, revtex, 7 figures. v1:Submitted to PRE. v2:considerably
reduced redundancy of presentation. v3:final version to appear in Phys.Rev.
Finite Size and Current Effects on IV Characteristics of Josephson Junction Arrays
The effects of finite size and of finite current on the current-voltage
characteristics of Josephson junction arrays is studied both theoretically and
by numerical simulations. The cross-over from non-linear to linear behavior at
low temperature is shown to be a finite size effect and the non-linear behavior
at higher temperature, , is shown to be a finite current effect.
These are argued to result from competition between the three length scales
characterizing the system. The importance of boundary effects is discussed and
it is shown that these may dominate the behavior in small arrays.Comment: 5 pages, figures included, to appear in PR
Medium-range interactions and crossover to classical critical behavior
We study the crossover from Ising-like to classical critical behavior as a
function of the range R of interactions. The power-law dependence on R of
several critical amplitudes is calculated from renormalization theory. The
results confirm the predictions of Mon and Binder, which were obtained from
phenomenological scaling arguments. In addition, we calculate the range
dependence of several corrections to scaling. We have tested the results in
Monte Carlo simulations of two-dimensional systems with an extended range of
interaction. An efficient Monte Carlo algorithm enabled us to carry out
simulations for sufficiently large values of R, so that the theoretical
predictions could actually be observed.Comment: 16 pages RevTeX, 8 PostScript figures. Uses epsf.sty. Also available
as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm
Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm
are discussed. Enhancements of this algorithm are illustrated by applications
to several phase transitions in lattice spin models. We demonstrate how the
statistical noise can be reduced considerably by a similarity transformation of
the transfer matrix using a variational estimate of its leading eigenvector, in
analogy with a common practice in various quantum Monte Carlo techniques. Here
we take the two-dimensional coupled -Ising model as an example.
Furthermore, we calculate interface free energies of finite three-dimensional
O() models, for the three cases , 2 and 3. Application of finite-size
scaling to the numerical results yields estimates of the critical points of
these three models. The statistical precision of the estimates is satisfactory
for the modest amount of computer time spent
Structure of wavefunctions in (1+2)-body random matrix ensembles
Abstrtact: Random matrix ensembles defined by a mean-field one-body plus a
chaos generating random two-body interaction (called embedded ensembles of
(1+2)-body interactions) predict for wavefunctions, in the chaotic domain, an
essentially one parameter Gaussian forms for the energy dependence of the
number of principal components NPC and the localization length {\boldmath
l}_H (defined by information entropy), which are two important measures of
chaos in finite interacting many particle systems. Numerical embedded ensemble
calculations and nuclear shell model results, for NPC and {\boldmath l}_H,
are compared with the theory. These analysis clearly point out that for
realistic finite interacting many particle systems, in the chaotic domain,
wavefunction structure is given by (1+2)-body embedded random matrix ensembles.Comment: 20 pages, 3 figures (1a-c, 2a-b, 3a-c), prepared for the invited talk
given in the international conference on `Perspectives in Theoretical
Physics', held at Physical Research Laboratory, Ahmedabad during January
8-12, 200
Domain Walls Motion and Resistivity in a Fully-Frustrated Josephson Array
It is identified numerically that the resistivity of a fully-frustrated
Josephson-junction array is due to motion of domain walls in vortex lattice
rather than to motion of single vortices
Edge effects in a frustrated Josephson junction array with modulated couplings
A square array of Josephson junctions with modulated strength in a magnetic
field with half a flux quantum per plaquette is studied by analytic arguments
and dynamical simulations. The modulation is such that alternate columns of
junctions are of different strength to the rest. Previous work has shown that
this system undergoes an XY followed by an Ising-like vortex lattice
disordering transition at a lower temperature. We argue that resistance
measurements are a possible probe of the vortex lattice disordering transition
as the linear resistance with
at intermediate temperatures due to dissipation at the array
edges for a particular geometry and vanishes for other geometries. Extensive
dynamical simulations are performed which support the qualitative physical
arguments.Comment: 8 pages with figs, RevTeX, to appear in Phys. Rev.
Vortex dynamics for two-dimensional XY models
Two-dimensional XY models with resistively shunted junction (RSJ) dynamics
and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is
verified that the vortex response is well described by the Minnhagen
phenomenology for both types of dynamics. Evidence is presented supporting that
the dynamical critical exponent in the low-temperature phase is given by
the scaling prediction (expressed in terms of the Coulomb gas temperature
and the vortex renormalization given by the dielectric constant
) both for RSJ and TDGL
and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature
phase. The results are discussed and compared with the results of other recent
papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio