Exchange frequencies in two - dimensional solids

In quantum solids composed of fermion particles, such as helium-3 and electrons, the low-temperature physics is governed by spin exchanges, according to the Thouless theory. We present path integral Monte Carlo calculations of ring exchange energies on ‘clean’ two-dimensional crystals of both helium-3 and electrons. We see a remarkable similarity of the results for these two ‘opposite’ systems. They are both ferromagnetic in the semi-classical limit (strong coupling) and antiferromagnetic near the melting transition where the relative exchange energies become equivalent. We focus here on the importance of long-ring exchanges near the melting transition. The total energy associated to exchanges may diverge, leading to a possible mechanism for the melting transition. (Some figures in this article are in colour only in the electronic version)