18 research outputs found
Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
We simulate self-avoiding walks on a cubic lattice and determine the second
virial coefficient for walks of different lengths. This allows us to determine
the critical value of the renormalized four-point coupling constant in the
three-dimensional N-vector universality class for N=0. We obtain g* =
1.4005(5), where g is normalized so that the three-dimensional
field-theoretical beta-function behaves as \beta(g) = - g + g^2 for small g. As
a byproduct, we also obtain precise estimates of the interpenetration ratio
Psi*, Psi* = 0.24685(11), and of the exponent \nu, \nu = 0.5876(2).Comment: 16 page
Simulations of grafted polymers in a good solvent
We present improved simulations of three-dimensional self avoiding walks with
one end attached to an impenetrable surface on the simple cubic lattice. This
surface can either be a-thermal, having thus only an entropic effect, or
attractive. In the latter case we concentrate on the adsorption transition, We
find clear evidence for the cross-over exponent to be smaller than 1/2, in
contrast to all previous simulations but in agreement with a re-summed field
theoretic -expansion. Since we use the pruned-enriched Rosenbluth
method (PERM) which allows very precise estimates of the partition sum itself,
we also obtain improved estimates for all entropic critical exponents.Comment: 5 pages with 9 figures included; minor change
The Path Integral Monte Carlo Calculation of Electronic Forces
We describe a method to evaluate electronic forces by Path Integral Monte
Carlo (PIMC). Electronic correlations, as well as thermal effects, are included
naturally in this method. For fermions, a restricted approach is used to avoid
the ``sign'' problem. The PIMC force estimator is local and has a finite
variance. We applied this method to determine the bond length of H and the
chemical reaction barrier of H+HH+H. At low
temperature, good agreement is obtained with ground state calculations. We
studied the proton-proton interaction in an electron gas as a simple model for
hydrogen impurities in metals. We calculated the force between the two protons
at two electronic densities corresponding to Na () and Al
() using a supercell with 38 electrons. The result is compared to
previous calculations. We also studied the effect of temperature on the
proton-proton interaction. At very high temperature, our result agrees with the
Debye screening of electrons. As temperature decreases, the Debye theory fails
both because of the strong degeneracy of electrons and most importantly, the
formation of electronic bound states around the protons.Comment: 18 pages, 10 figure
Scaling of Star Polymers with one to 80 Arms
We present large statistics simulations of 3-dimensional star polymers with
up to arms, and with up to 4000 monomers per arm for small values of
. They were done for the Domb-Joyce model on the simple cubic lattice. This
is a model with soft core exclusion which allows multiple occupancy of sites
but punishes each same-site pair of monomers with a Boltzmann factor . We
use this to allow all arms to be attached at the central site, and we use the
`magic' value to minimize corrections to scaling. The simulations are
made with a very efficient chain growth algorithm with resampling, PERM,
modified to allow simultaneous growth of all arms. This allows us to measure
not only the swelling (as observed from the center-to-end distances), but also
the partition sum. The latter gives very precise estimates of the critical
exponents . For completeness we made also extensive simulations of
linear (unbranched) polymers which give the best estimates for the exponent
.Comment: 7 pages, 7 figure
Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice
We present a high-statistics Monte Carlo determination of the exponent gamma
for self-avoiding walks on a Manhattan lattice in two dimensions. A
conservative estimate is \gamma \gtapprox 1.3425(3), in agreement with the
universal value 43/32 on regular lattices, but in conflict with predictions
from conformal field theory and with a recent estimate from exact enumerations.
We find strong corrections to scaling that seem to indicate the presence of a
non-analytic exponent Delta < 1. If we assume Delta = 11/16 we find gamma =
1.3436(3), where the error is purely statistical.Comment: 24 pages, LaTeX2e, 4 figure
Critical Exponents of the N-vector model
Recently the series for two RG functions (corresponding to the anomalous
dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been
extended to next order (seven loops) by Murray and Nickel. We examine here the
influence of these additional terms on the estimates of critical exponents of
the N-vector model, using some new ideas in the context of the Borel summation
techniques. The estimates have slightly changed, but remain within errors of
the previous evaluation. Exponents like eta (related to the field anomalous
dimension), which were poorly determined in the previous evaluation of Le
Guillou--Zinn-Justin, have seen their apparent errors significantly decrease.
More importantly, perhaps, summation errors are better determined. The change
in exponents affects the recently determined ratios of amplitudes and we report
the corresponding new values. Finally, because an error has been discovered in
the last order of the published epsilon=4-d expansions (order epsilon^5), we
have also reanalyzed the determination of exponents from the epsilon-expansion.
The conclusion is that the general agreement between epsilon-expansion and 3D
series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references
update
Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"
New estimates of the critical exponents have been obtained from the
field-theoretical renormalization group using a new method for summing
divergent series. The results almost coincide with the central values obtained
by Le Guillou and Zinn-Justin (the so-called "standard values"), but have lower
uncertainty. It has been shown that usual field-theoretical estimates
implicitly imply the smoothness of the coefficient functions. The last
assumption is open for discussion in view of the existence of the oscillating
contribution to the coefficient functions. The appropriate interpretation of
the last contribution is necessary both for the estimation of the systematic
errors in the "standard values" and for a further increase in accuracy.Comment: PDF, 12 page
Crossover scaling from classical to non-classical critical behaviour
Interacting physical systems in the neighborhood of criticality (and massive
continuum field theories) can often be characterized by just two physical
scales: a (macroscopic) correlation length and a (microscopic) interaction
range, related to the coupling and measured by the Ginzburg number . A
critical crossover limit can be defined when both scales become large while
their ratio stays finite. The corresponding scaling functions are universal,
and they are related to the standard field-theory renormalization-group
functions. The critical crossover describes the unique flow from the Gaussian
to the nonclassical fixed point