4 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
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
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