  We prove several results of concentration for eigenfunctions in Toeplitz
quantization. With mild assumptions on the regularity, we prove that
eigenfunctions are $O(exp(-cN^{\delta}))$ away from the corresponding level set
of the symbol, where N is the inverse semiclassical parameter and $0 < \delta <
1$ depends on the regularity. As an application, we prove a precise bound for
the free energy of spin systems at high temperatures, sharpening a result of
Lieb.
