313 research outputs found
The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
We study the classical XY (plane rotator) model at the Kosterlitz-Thouless
phase transition. We simulate the model using the single cluster algorithm on
square lattices of a linear size up to L=2048.We derive the finite size
behaviour of the second moment correlation length over the lattice size
xi_{2nd}/L at the transition temperature. This new prediction and the analogous
one for the helicity modulus are confronted with our Monte Carlo data. This way
beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we
address the puzzle of logarithmic corrections of the magnetic susceptibility
chi at the transition temperature.Comment: Monte Carlo results for xi/L in table 1 and 2 corrected. Due to a
programming error,these numbers were wrong by about a factor 1+1/L^2.
Correspondingly the fits with L_min=64 and 128 given in table 5 and 6 are
changed by little.The central results of the paper are not affected. Wrong
sign in eq.(52) corrected. Appendix extende
Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model
on the three-dimensional simple cubic lattice with nearest neighbour
interactions. For this purpose, we use Monte Carlo simulations in connection
with a finite size scaling method. We find that there exists a finite value of
the coupling lambda^*, for both values of N, where leading corrections to
scaling vanish. As a first application, we compute the critical exponents
nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for
N=4.Comment: 21 pages, 2 figure
The critical exponents of the superfluid transition in He4
We improve the theoretical estimates of the critical exponents for the
three-dimensional XY universality class, which apply to the superfluid
transition in He4 along the lambda-line of its phase diagram. We obtain the
estimates alpha=-0.0151(3), nu=0.6717(1), eta=0.0381(2), gamma=1.3178(2),
beta=0.3486(1), and delta=4.780(1). Our results are obtained by finite-size
scaling analyses of high-statistics Monte Carlo simulations up to lattice size
L=128 and resummations of 22nd-order high-temperature expansions of two
improved models with suppressed leading scaling corrections. We note that our
result for the specific-heat exponent alpha disagrees with the most recent
experimental estimate alpha=-0.0127(3) at the superfluid transition of He4 in
microgravity environment.Comment: 45 pages, 16 fig
Critical behavior of the compact 3d U(1) theory in the limit of zero spatial coupling
Critical properties of the compact three-dimensional U(1) lattice gauge
theory are explored at finite temperatures on an asymmetric lattice. For
vanishing value of the spatial gauge coupling one obtains an effective
two-dimensional spin model which describes the interaction between Polyakov
loops. We study numerically the effective spin model for N_t=1,4,8 on lattices
with spatial extension ranging from L=64 to L=256. Our results indicate that
the finite-temperature U(1) lattice gauge theory belongs to the universality
class of the two-dimensional XY model, thus supporting the Svetitsky-Yaffe
conjecture.Comment: 17 pages, 5 figures; two references added, a few comments included,
title changed; version to appear on J. Stat. Mec
The three-dimensional XY universality class: A high precision Monte Carlo estimate of the universal amplitude ratio A_+/A_-
We simulate the improved three-dimensional two-component phi^4 model on the
simple cubic lattice in the low and the high temperature phase for reduced
temperatures down to |T-T_c|/T_c \approx 0.0017 on lattices of a size up to
350^3. Our new results for the internal energy and the specific heat are
combined with the accurate estimates of beta_c and data for the internal energy
and the specific heat at \beta_c recently obtained in cond-mat/0605083. We find
R_{\alpha} = (1-A_+/A_-)/\alpha = 4.01(5), where alpha is the critical exponent
of the specific heat and A_{\pm} is the amplitude of the specific heat in the
high and the low temperature phase, respectively.Comment: 14 pages, 4 figure
Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point
We study the self-averaging properties of the three dimensional site diluted
Heisenberg model. The Harris criterion \cite{critharris} states that disorder
is irrelevant since the specific heat critical exponent of the pure model is
negative. According with some analytical approaches \cite{harris}, this implies
that the susceptibility should be self-averaging at the critical temperature
(). We have checked this theoretical prediction for a large range of
dilution (including strong dilution) at critically and we have found that the
introduction of scaling corrections is crucial in order to obtain
self-averageness in this model. Finally we have computed critical exponents and
cumulants which compare very well with those of the pure model supporting the
Universality predicted by the Harris criterion.Comment: 11 pages, 11 figures, 14 tables. New analysis (scaling corrections in
the g2=0 scenario) and new numerical simulations. Title and conclusions
chang
Multicritical behavior in the fully frustrated XY model and related systems
We study the phase diagram and critical behavior of the two-dimensional
square-lattice fully frustrated XY model (FFXY) and of two related models, a
lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the
critical modes of the FFXY model, and a coupled Ising-XY model. We present a
finite-size-scaling analysis of the results of high-precision Monte Carlo
simulations on square lattices L x L, up to L=O(10^3).
In the FFXY model and in the other models, when the transitions are
continuous, there are two very close but separate transitions. There is an
Ising chiral transition characterized by the onset of chiral long-range order
while spins remain paramagnetic. Then, as temperature decreases, the systems
undergo a Kosterlitz-Thouless spin transition to a phase with quasi-long-range
order.
The FFXY model and the other models in a rather large parameter region show a
crossover behavior at the chiral and spin transitions that is universal to some
extent. We conjecture that this universal behavior is due to a multicritical
point. The numerical data suggest that the relevant multicritical point is a
zero-temperature transition. A possible candidate is the O(4) point that
controls the low-temperature behavior of the 4-vector model.Comment: 62 page
The specific heat of thin films near the lambda-transition: A Monte Carlo study of an improved three-dimensional lattice model
We study the finite size scaling behaviour of the specific heat of thin films
in the neighbourhood of the lambda-transition. To this end we have simulated
the improved two-component phi^4 model on the simple cubic lattice. We employ
free boundary conditions in the short direction to mimic the vanishing order
parameter at the boundaries of a 4He film. Most of our simulations are
performed for the thicknesses L_0=8,16 and 32 of the film. It turns out that
one has to take into account corrections proportional 1/L_0 to obtain a good
collapse of the finite size scaling functions obtained from different L_0. Our
results are compared with those obtained from experiments on thin films of 4He
near the lambda-transition, from field theory and from previous Monte Carlo
simulations.Comment: 46 pages, 15 figure
The thermodynamic Casimir effect in the neighbourhood of the lambda-transition: A Monte Carlo study of an improved three dimensional lattice model
We study the thermodynamic Casimir effect in thin films in the three
dimensional XY universality class. To this end, we simulate the improved two
component phi^4 model on the simple cubic lattice. We use lattices up to the
thickness L_0=33. Based on the results of our Monte Carlo simulations we
compute the universal finite size scaling function theta that characterizes the
behaviour of the thermodynamic Casimir force in the neighbourhood of the
critical point. We confirm that leading corrections to the universal finite
size scaling behaviour due to free boundary conditions can be expressed by an
effective thickness L_{0,eff} = L_0+ L_s, with L_s =1.02(7). Our results are
compared with experiments on films of 4He near the lambda-transition, previous
Monte Carlo simulations of the XY model on the simple cubic lattice and
field-theoretic results. Our result for the finite size scaling function theta
is essentially consistent with the experiments on films of 4He and the previous
Monte Carlo simulations.Comment: 23 pages, 5 figure
- …