The following formula gives the critical coupling (more precisely the ratio of the spin-spin coupling over the temperature) for $O(n)$ models on a triangular lattice:

$$\text{e}^{-2K}=\frac{1}{\sqrt{2+\sqrt{2-n}}}$$

with $K=\beta J$

Numerically, it says that:

Ising model (n = 1) has $K \approx 0.27$

XY model (n=2) has $K \approx 0.17$

Thus, the critical temperature for the XY model is higher than the Ising model. I've been thinking about it but I can't come out with a reason of why allowing the order parameter to take continuous values means that we need to go higher in temperature to destroy order. Is there a (semi) intuitive reason for that?

This post imported from StackExchange Physics at 2014-06-29 09:38 (UCT), posted by SE-user Learning is a mess