392 research outputs found
Depinning Transition of a Two Dimensional Vortex Lattice in a Commensurate Periodic Potential
We use Monte Carlo simulations of the 2D one component Coulomb gas on a
triangular lattice, to study the depinning transition of a 2D vortex lattice in
a commensurate periodic potential. A detailed finite size scaling analysis
indicates this transition to be first order. No significant changes in behavior
were found as vortex density was varied over a wide range.Comment: 5 pages, 8 figures. Revised discussion of correlation length exponent
using a more accurate finite size scaling analysis. New figs. 5 and 6. Old
figs. 6 and 7 now figs. 7 and
Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond 8-state Potts Model
The self-dual random-bond eight-state Potts model is studied numerically
through large-scale Monte Carlo simulations using the Swendsen-Wang cluster
flipping algorithm. We compute bulk and surface order parameters and
susceptibilities and deduce the corresponding critical exponents at the random
fixed point using standard finite-size scaling techniques. The scaling laws are
suitably satisfied. We find that a belonging of the model to the 2D Ising model
universality class can be conclusively ruled out, and the dimensions of the
relevant bulk and surface scaling fields are found to take the values
, , , to be compared to their Ising values:
15/8, 1, and 1/2.Comment: LaTeX file with Revtex, 4 pages, 4 eps figures, to appear in Phys.
Rev. Let
SURFACE INDUCED FINITE-SIZE EFFECTS FOR FIRST ORDER PHASE TRANSITIONS
We consider classical lattice models describing first-order phase
transitions, and study the finite-size scaling of the magnetization and
susceptibility. In order to model the effects of an actual surface in systems
like small magnetic clusters, we consider models with free boundary conditions.
For a field driven transition with two coexisting phases at the infinite volume
transition point , we prove that the low temperature finite volume
magnetization m_{\free}(L,h) per site in a cubic volume of size behaves
like
m_\free(L,h)=\frac{m_++m_-}2 + \frac{m_+-m_-}2
\tanh \bigl(\frac{m_+-m_-}2\,L^d\, (h-h_\chi(L))\bigr)+O(1/L),
where is the position of the maximum of the (finite volume)
susceptibility and are the infinite volume magnetizations at
and , respectively. We show that is shifted by an amount
proportional to with respect to the infinite volume transitions point
provided the surface free energies of the two phases at the transition
point are different. This should be compared with the shift for periodic boun\-
dary conditons, which for an asymmetric transition with two coexisting phases
is proportional only to . One also consider the position of
the maximum of the so called Binder cummulant U_\free(L,h). While it is again
shifted by an amount proportional to with respect to the infinite volume
transition point , its shift with respect to is of the much
smaller order . We give explicit formulas for the proportionality
factors, and show that, in the leading term, the relative shift is
the same as that for periodic boundary conditions.Comment: 65 pages, amstex, 1 PostScript figur
Interplay of quantum and thermal fluctuations in a frustrated magnet
We demonstrate the presence of an extended critical phase in the transverse
field Ising magnet on the triangular lattice, in a regime where both thermal
and quantum fluctuations are important. We map out a complete phase diagram by
means of quantum Monte Carlo simulations, and find that the critical phase is
the result of thermal fluctuations destabilising an order established by the
quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions
from the paramagnet on one hand and the quantum-fluctuation driven
three-sublattice ordered phase on the other. Our work provides further evidence
that the zero temperature quantum phase transition is in the 3d XY universality
class.Comment: 9 pages, revtex
Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice
We study the anti-ferromagnetic six-state clock model with nearest neighbor
interactions on a triangular lattice with extensive Monte-Carlo simulations. We
find clear indications of two phase transitions at two different temperatures:
Below a chirality order sets in and by a thorough finite size scaling
analysis of the specific heat and the chirality correlation length we show that
this transition is in the Ising universality class (with a non-vanishing
chirality order parameter below ). At the spin-spin
correlation length as well as the spin susceptibility diverges according to a
Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below
. We compare our results to recent x-ray diffraction experiments on the
orientational ordering of CFBr monolayers physisorbed on graphite. We argue
that the six-state clock model describes the universal feature of the phase
transition in the experimental system and that the orientational ordering
belongs to the KT universality class.Comment: 8 pages, 9 figure
First-Order Phase Transition with Breaking of Lattice Rotation Symmetry in Continuous-Spin Model on Triangular Lattice
Using a Monte Carlo method, we study the finite-temperature phase transition
in the two-dimensional classical Heisenberg model on a triangular lattice with
or without easy-plane anisotropy. The model takes account of competing
interactions: a ferromagnetic nearest-neighbor interaction and an
antiferromagnetic third nearest-neighbor interaction . As a result, the
ground state is a spiral spin configuration for . In this
structure, global spin rotation cannot compensate for the effect of 120-degree
lattice rotation, in contrast to the conventional 120-degree structure of the
nearest-neighbor interaction model. We find that this model exhibits a
first-order phase transition with breaking of the lattice rotation symmetry at
a finite temperature. The transition is characterized as a vortex
dissociation in the isotropic case, whereas it can be viewed as a vortex
dissociation in the anisotropic case. Remarkably, the latter is continuously
connected to the former as the magnitude of anisotropy decreases, in contrast
to the recent work by Misawa and Motome [J. Phys. Soc. Jpn. \textbf{79} (2010)
073001.] in which both the transitions were found to be continuous.Comment: 11pages, 16figures, accepted to JPS
Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?
In extensive Monte Carlo simulations the phase transition of the random field
Ising model in three dimensions is investigated. The values of the critical
exponents are determined via finite size scaling. For a Gaussian distribution
of the random fields it is found that the correlation length diverges
with an exponent at the critical temperature and that
with for the connected susceptibility
and with for
the disconnected susceptibility. Together with the amplitude ratio
being close to one this gives
further support for a two exponent scaling scenario implying
. The magnetization behaves discontinuously at the
transition, i.e. , indicating a first order transition. However, no
divergence for the specific heat and in particular no latent heat is found.
Also the probability distribution of the magnetization does not show a
multi-peak structure that is characteristic for the phase-coexistence at first
order phase transition points.Comment: 14 pages, RevTeX, 11 postscript figures (fig9.ps and fig11.ps should
be printed separately
Aperiodicity-Induced Second-Order Phase Transition in the 8-State Potts Model
We investigate the critical behavior of the two-dimensional 8-state Potts
model with an aperiodic distribution of the exchange interactions between
nearest-neighbor rows. The model is studied numerically through intensive Monte
Carlo simulations using the Swendsen-Wang cluster algorithm. The transition
point is located through duality relations, and the critical behavior is
investigated using FSS techniques at criticality. For strong enough
fluctuations of the aperiodic sequence under consideration, a second order
phase transition is found. The exponents and are
obtained at the new fixed point.Comment: LaTeX file with Revtex, 4 pages, 5 eps figures, to appear in Phys.
Rev. Let
Universal Short-Time Dynamics in the Kosterlitz-Thouless Phase
We study the short-time dynamics of systems that develop ``quasi long-range
order'' after a quench to the Kosterlitz-Thouless phase. With the working
hypothesis that the ``universal short-time behavior'', previously found in
Ising-like systems, also occurs in the Kosterlitz-Thouless phase, we explore
the scaling behavior of thermodynamic variables during the relaxational process
following the quench. As a concrete example, we investigate the two-dimensional
-state clock model by Monte Carlo simulation. The exponents governing the
magnetization, the second moment, and the autocorrelation function are
calculated. From them, by means of scaling relations, estimates for the
equilibrium exponents and are derived. In particular, our estimates
for the temperature-dependent anomalous dimension that governs the
static correlation function are consistent with existing analytical and
numerical results and, thus, confirm our working hypothesis.Comment: 16 pages, 9 postscript figures, REVTEX 3.0, submitted to Phys. Rev.
Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries
We present a numerical study of 2D random-bond Potts ferromagnets. The model
is studied both below and above the critical value which discriminates
between second and first-order transitions in the pure system. Two geometries
are considered, namely cylinders and square-shaped systems, and the critical
behavior is investigated through conformal invariance techniques which were
recently shown to be valid, even in the randomness-induced second-order phase
transition regime Q>4. In the cylinder geometry, connectivity transfer matrix
calculations provide a simple test to find the range of disorder amplitudes
which is characteristic of the disordered fixed point. The scaling dimensions
then follow from the exponential decay of correlations along the strip. Monte
Carlo simulations of spin systems on the other hand are generally performed on
systems of rectangular shape on the square lattice, but the data are then
perturbed by strong surface effects. The conformal mapping of a semi-infinite
system inside a square enables us to take into account boundary effects
explicitly and leads to an accurate determination of the scaling dimensions.
The techniques are applied to different values of Q in the range 3-64.Comment: LaTeX2e file with Revtex, revised versio
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