Criterion for dominance of directional over size fluctuations in destroying order

For systems that exhibit a second-order phase transition with a spontaneously broken continuous O(N) symmetry at low temperatures, 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 become important.