Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0

Details Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0 Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0

2007-03-05

arxiv.org/abs/cond-mat/0703114v1

J.Phys.A40:F539,2007; J.Phys.A40:F539-F550,2007

Physics

Condensed Matter

Statistical Mechanics

16 pages

Scientific paper

10.1088/1751-8113/40/26/F05

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).

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