Criterion for Dominance of Directional over Size Fluctuations in Destroying Order

TL;DR

This paper establishes a criterion to determine when directional fluctuations, rather than size fluctuations, destroy order in systems with second-order phase transitions and broken continuous symmetry, especially near the critical temperature.

Contribution

It introduces a new criterion for identifying the temperature at which directional fluctuations dominate over size fluctuations in destroying order.

Findings

T_K is always below T_G, indicating directional fluctuations become critical earlier.

Provides a quantitative criterion for the dominance of directional fluctuations.

Enhances understanding of fluctuation roles near phase transition points.

Abstract

For systems exhibiting a second-order phase transition with a spontaneously broken continuous O(N)-symmetry at low temperature, we give a criterion for judging at which temperature T_K long-range directional fluctuations of the order field destroy the order when approaching the critical temperature from below. The temperature T_K lies always significantly below the famous Ginzburg temperature T_G at which size fluctuations of finite range in the order field become important.