724 research outputs found
Monte Carlo Study of Topological Defects in the 3D Heisenberg Model
We use single-cluster Monte Carlo simulations to study the role of
topological defects in the three-dimensional classical Heisenberg model on
simple cubic lattices of size up to . By applying reweighting techniques
to time series generated in the vicinity of the approximate infinite volume
transition point , we obtain clear evidence that the temperature
derivative of the average defect density behaves
qualitatively like the specific heat, i.e., both observables are finite in the
infinite volume limit. This is in contrast to results by Lau and Dasgupta [{\em
Phys. Rev.\/} {\bf B39} (1989) 7212] who extrapolated a divergent behavior of
at from simulations on lattices of size up to
. We obtain weak evidence that scales with the
same critical exponent as the specific heat.As a byproduct of our simulations,
we obtain a very accurate estimate for the ratio of the
specific-heat exponent with the correlation-length exponent from a finite-size
scaling analysis of the energy.Comment: pages ,4 ps-figures not included, FUB-HEP 10/9
Correlations in the low-temperature phase of the two-dimensional XY model
Monte Carlo simulations of the two-dimensional XY model are performed in a
square geometry with fixed boundary conditions. Using a conformal mapping it is
very easy to deduce the exponent eta_sigma(T) of the order parameter
correlation function at any temperature in the critical phase of the model. The
temperature behaviour of eta_sigma(T) is obtained numerically with a good
accuracy up to the Kosterlitz-Thouless transition temperature. At very low
temperatures, a good agreement is found with Berezinskii's harmonic
approximation. Surprisingly, we show some evidence that there are no
logarithmic corrections to the behaviour of the order parameter density profile
(with symmetry breaking surface fields) at the Kosterlitz-Thouless transition
temperature.Comment: 7 pages, 2 eps figure
Geometric properties of two-dimensional O(n) loop configurations
We study the fractal geometry of O() loop configurations in two dimensions
by means of scaling and a Monte Carlo method, and compare the results with
predictions based on the Coulomb gas technique. The Monte Carlo algorithm is
applicable to models with noninteger and uses local updates. Although these
updates typically lead to nonlocal modifications of loop connectivities, the
number of operations required per update is only of order one. The Monte Carlo
algorithm is applied to the O() model for several values of , including
noninteger ones. We thus determine scaling exponents that describe the fractal
nature of O() loops at criticality. The results of the numerical analysis
agree with the theoretical predictions.Comment: 18 pages, 6 figure
Monte Carlo Simulation of the Short-time Behaviour of the Dynamic XY Model
Dynamic relaxation of the XY model quenched from a high temperature state to
the critical temperature or below is investigated with Monte Carlo methods.
When a non-zero initial magnetization is given, in the short-time regime of the
dynamic evolution the critical initial increase of the magnetization is
observed. The dynamic exponent is directly determined. The results
show that the exponent varies with respect to the temperature.
Furthermore, it is demonstrated that this initial increase of the magnetization
is universal, i.e. independent of the microscopic details of the initial
configurations and the algorithms.Comment: 14 pages with 5 figures in postscrip
The Critical Properties of Two-dimensional Oscillator Arrays
We present a renormalization group study of two dimensional arrays of
oscillators, with dissipative, short range interactions. We consider the case
of non-identical oscillators, with distributed intrinsic frequencies within the
array and study the steady-state properties of the system. In two dimensions no
macroscopic mutual entrainment is found but, for identical oscillators,
critical behavior of the Berezinskii-Kosterlitz-Thouless type is shown to be
present. We then discuss the stability of (BKT) order in the physical case of
distributed quenched random frequencies. In order to do that, we show how the
steady-state dynamical properties of the two dimensional array of non-identical
oscillators are related to the equilibrium properties of the XY model with
quenched randomness, that has been already studied in the past. We propose a
novel set of recursion relations to study this system within the Migdal
Kadanoff renormalization group scheme, by mean of the discrete clock-state
formulation. We compute the phase diagram in the presence of random dissipative
coupling, at finite values of the clock state parameter. Possible experimental
applications in two dimensional arrays of microelectromechanical oscillators
are briefly suggested.Comment: Contribution to the conference "Viewing the World through Spin
Glasses" in honour of Professor David Sherrington on the occasion of his 65th
birthda
Monte Carlo Study of the Anisotropic Heisenberg Antiferromagnet on the Triangular Lattice
We report a Monte Carlo study of the classical antiferromagnetic Heisenberg
model with easy axis anisotropy on the triangular lattice. Both the free energy
cost for long wavelength spin waves as well as for the formation of free
vortices are obtained from the spin stiffness and vorticity modulus
respectively. Evidence for two distinct Kosterlitz-Thouless types of
defect-mediated phase transitions at finite temperatures is presented.Comment: 8 pages, 10 figure
The Heisenberg antiferromagnet on a triangular lattice: topological excitations
We study the topological defects in the classical Heisenberg antiferromagnet
in two dimensions on a triangular lattice (HAFT). While the topological
analysis of the order parameter space indicates that the defects are of
type, consideration of the energy leads us to a description of the low--energy
stationary points of the action in terms of vortices, as in the planar XY
model. Starting with the continuum description of the HAFT, we show
analytically that its partition function can be reduced to that of a
2--dimensional Coulomb gas with logarithmic interaction. Thus, at low
temperatures, the correlation length is determined by the spinwaves, while at
higher temperatures we expect a crossover to a Kosterlitz--Thouless type
behaviour. The results of recent Monte Carlo calculations of the correlation
length are consistent with such a crossover.Comment: 9 pages, revtex, preprint: ITP-UH 03/9
A numerical renormalization group study of laser induced freezing
We study the phenomenon of laser induced freezing, within a numerical
renormalization scheme which allows explicit comparison with a recent defect
mediated melting theory. Precise values for the `bare' dislocation fugacities
and elastic moduli of the 2-d hard disk system are obtained from a constrained
Monte Carlo simulation sampling only configurations {\em without} dislocations.
These are used as inputs to appropriate renormalization flow equations to
obtain the equilibrium phase diagram which shows excellent agreement with
earlier simulation results. We show that the flow equations need to be correct
at least up to third order in defect fugacity to reproduce meaningful results.Comment: Minor Corrections; Combined version of Europhys. Lett. 67 (2004) p.
814 and Europhys. Lett. 68 (2004) p. 16
Phase Transition of XY Model in Heptagonal Lattice
We numerically investigate the nature of the phase transition of the XY model
in the heptagonal lattice with the negative curvature, in comparison to other
interaction structures such as a flat two-dimensional (2D) square lattice and a
small-world network. Although the heptagonal lattice has a very short
characteristic path length like the small-world network structure, it is
revealed via calculation of the Binder's cumulant that the former exhibits a
zero-temperature phase transition while the latter has the finite-temperature
transition of the mean-field nature. Through the computation of the vortex
density as well as the correlation function in the low-temperature
approximation, we show that the absence of the phase transition originates from
the strong spinwave-type fluctuation, which is discussed in relation to the
usual 2D XY model.Comment: 5 pages, 6 figures, to be published in Europhys. Let
Phase Transitions in Hexane Monolayers Physisorbed onto Graphite
We report the results of molecular dynamics (MD) simulations of a complete
monolayer of hexane physisorbed onto the basal plane of graphite. At low
temperatures the system forms a herringbone solid. With increasing temperature,
a solid to nematic liquid crystal transition takes place at K
followed by another transition at K into an isotropic fluid.
We characterize the different phases by calculating various order parameters,
coordinate distributions, energetics, spreading pressure and correlation
functions, most of which are in reasonable agreement with available
experimental evidence. In addition, we perform simulations where the
Lennard-Jones interaction strength, corrugation potential strength and dihedral
rigidity are varied in order to better characterize the nature of the two
transitions through. We find that both phase transitions are facilitated by a
``footprint reduction'' of the molecules via tilting, and to a lesser degree
via creation of gauche defects in the molecules.Comment: 18 pages, eps figures embedded, submitted to Phys. Rev.
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