Universal amplitudes of power-law tails in the asymptotic structure factor of systems with topological defects.

Abstract

We compute the asymptotic structure factor S(k,t) of the O(n) model for n\ensuremath{\le}d, where d and n are the dimensions of space and of the order parameter, respectively. Topological defects in the field lead to the power-law tail S(k,t)=A(n,d)\ensuremath{\rho}(t)${\mathit{k}}^{\mathrm{\ensuremath{-}}(\mathit{d}+\mathit{n})}$, where \ensuremath{\rho} is the defect density. The amplitude A(n,d) is calculated exactly using purely geometrical arguments based on the defect field.