Phase Ordering Dynamics of the O(n) Model - Exact Predictions and Numerical Results

TL;DR

This paper provides exact predictions and numerical validation for the phase ordering dynamics of the $O(n)$ model, revealing limitations of the scaling hypothesis in certain cases.

Contribution

It derives exact short-distance singularities of correlation functions in the $O(n)$ model and compares them with numerical results, highlighting where the scaling hypothesis fails.

Findings

Exact short-distance singularities derived

Numerical results confirm predictions in most cases

Scaling hypothesis does not hold for $d=2$, $O(2)$ model

Abstract

We consider the pair correlation functions of both the order parameter field and its square for phase ordering in the $O(n)$ model with nonconserved order parameter, in spatial dimension $2\le d\le 3$ and spin dimension $1\le n\le d$. We calculate, in the scaling limit, the exact short-distance singularities of these correlation functions and compare these predictions to numerical simulations. Our results suggest that the scaling hypothesis does not hold for the $d=2$ $O(2)$ model. Figures (23) are available on request - email bray@v2.ph.man.ac.uk