Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
arXiv:cond-mat/0703114 · doi:10.1088/1751-8113/40/26/F05
Abstract
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 β(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 ν, ν= 0.5876(2).
16 pages