10 research outputs found
The scaling region of the lattice O(N) sigma model at finite temperature
We present results from numerical studies of the finite temperature phase
transition of the O(N)-symmetric non-linear sigma model for
and 3. We study the dependence of the width of the 3d critical region on
and we show that the broken phase scaling region is much wider for N=2 and 3
than for N=1. We also compare the widths of the critical region in the low
and high phases of the O(2) model and we show that the scaling region in
the broken phase is much wider than in the symmetric phase. We also report
results for the width of the scaling regions in the low phase
Ising model and we show that the spatial correlation length has to be
approximately twice the lattice temporal extent before the 2d scaling region is
reached.Comment: 17 pages, 7 figure
Ising cubes with enhanced surface couplings
Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor
interactions and enhanced couplings between surface spins are studied. In
particular, at the surface transition, the corner magnetization shows
non-universal, coupling-dependent critical behavior in the thermodynamic limit.
Results on the critical exponent of the corner magnetization are compared to
previous findings on two-dimensional Ising models with three intersecting
defect lines.Comment: 4 pages, 2 figures included, submitted to Phys. Rev.
Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet
The two-dimensional random-bond Ising model is numerically studied on long
strips by transfer-matrix methods. It is shown that the rate of decay of
correlations at criticality, as derived from averages of the two largest
Lyapunov exponents plus conformal invariance arguments, differs from that
obtained through direct evaluation of correlation functions. The latter is
found to be, within error bars, the same as in pure systems. Our results
confirm field-theoretical predictions. The conformal anomaly is calculated
from the leading finite-width correction to the averaged free energy on strips.
Estimates thus obtained are consistent with , the same as for the pure
Ising model.Comment: RevTeX 3, 11 pages +2 figures, uuencoded, IF/UFF preprin
High precision Monte Carlo simulations of interfaces in the three-dimensional Ising model: a comparison with the Nambu-Goto effective string model
Motivated by the recent progress in the effective string description of the
interquark potential in lattice gauge theory, we study interfaces with periodic
boundary conditions in the three-dimensional Ising model. Our Monte Carlo
results for the associated free energy are compared with the next-to-leading
order (NLO) approximation of the Nambu-Goto string model. We find clear
evidence for the validity of the effective string model at the level of the NLO
truncation.Comment: 20 pages, 1 figur
Crossover and self-averaging in the two-dimensional site-diluted Ising model
Using the newly proposed probability-changing cluster (PCC) Monte Carlo
algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since
we can tune the critical point of each random sample automatically with the PCC
algorithm, we succeed in studying the sample-dependent and the sample
average of physical quantities at each systematically. Using the
finite-size scaling (FSS) analysis for , we discuss the importance of
corrections to FSS both in the strong-dilution and weak-dilution regions. The
critical phenomena of the 2D site-diluted Ising model are shown to be
controlled by the pure fixed point. The crossover from the percolation fixed
point to the pure Ising fixed point with the system size is explicitly
demonstrated by the study of the Binder parameter. We also study the
distribution of critical temperature . Its variance shows the power-law
dependence, , and the estimate of the exponent is consistent
with the prediction of Aharony and Harris [Phys. Rev. Lett. {\bf 77}, 3700
(1996)]. Calculating the relative variance of critical magnetization at the
sample-dependent , we show that the 2D site-diluted Ising model
exhibits weak self-averaging.Comment: 6 pages including 6 eps figures, RevTeX, to appear in Phys. Rev.
Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet
It is shown by Monte Carlo method that the finite size scaling (FSS) holds in
the two dimensional random-coupled Ising ferromagnet. It is also demonstrated
that the form of universal FSS function constructed via novel FSS scheme
depends on the strength of the random coupling for strongly disordered cases.
Monte Carlo measurements of thermodynamic (infinite volume limit) data of the
correlation length () up to along with measurements of
the fourth order cumulant ratio (Binder's ratio) at criticality are reported
and analyzed in view of two competing scenarios. It is demonstrated that the
data are almost exclusively consistent with the scenario of weak universality.Comment: 9 pages, 4figuer
Extension to order of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
Using a renormalized linked-cluster-expansion method, we have extended to
order the high-temperature series for the susceptibility
and the second-moment correlation length of the spin-1/2 Ising models on
the sc and the bcc lattices. A study of these expansions yields updated direct
estimates of universal parameters, such as exponents and amplitude ratios,
which characterize the critical behavior of and . Our best
estimates for the inverse critical temperatures are
and . For the
susceptibility exponent we get and for the correlation
length exponent we get .
The ratio of the critical amplitudes of above and below the critical
temperature is estimated to be . The analogous ratio for
is estimated to be . For the correction-to-scaling
amplitude ratio we obtain .Comment: Misprints corrected, 8 pages, latex, no figure
Ising model on 3D random lattices: A Monte Carlo study
We report single-cluster Monte Carlo simulations of the Ising model on
three-dimensional Poissonian random lattices with up to 128,000 approx. 503
sites which are linked together according to the Voronoi/Delaunay prescription.
For each lattice size quenched averages are performed over 96 realizations. By
using reweighting techniques and finite-size scaling analyses we investigate
the critical properties of the model in the close vicinity of the phase
transition point. Our random lattice data provide strong evidence that, for the
available system sizes, the resulting effective critical exponents are
indistinguishable from recent high-precision estimates obtained in Monte Carlo
studies of the Ising model and \phi^4 field theory on three-dimensional regular
cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure
One-dimensional incommensurate structures at finite temperatures
The problem of one-dimensional systems of adsorbed atoms at finite temperatures is considered. For any form of the periodic potential of a substrate and for any value of the initial incommensurate wave vector the exact formulae for the free energy and for the structural factor of scattering are obtained.On discute les propriétés thermodynamiques des systèmes unidimensionnels d'atomes adsorbés pour tout potentiel périodique du substrat. On obtient les formules exactes pour l'énergie libre et les facteurs de structure en fonction de la température et de la différence des périodes initiales du réseau des atomes adsorbés et du substrat