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

TL;DR

This paper uses lattice simulations of self-avoiding walks to accurately determine the renormalized four-point coupling constant and related critical parameters in the three-dimensional N=0 universality class.

Contribution

It provides the first precise estimate of the renormalized four-point coupling constant for N=0 in three dimensions using simulation data.

Findings

g* = 1.4005(5) for the coupling constant

Psi* = 0.24685(11) for the interpenetration ratio

nu = 0.5876(2) for the critical exponent

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 \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).