Spin Liquid in the Multiple-Spin Exchange Model on the Triangular Lattice: 3 He on Graphite

Using exact diagonalizations, we investigate the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ phase diagram of the multiple-spin exchange (MSE) model on the triangular lattice, we find a transition separating a ferromagnetic phase from a nonmagnetic gapped spin liquid phase. Systems far enough from the ferromagnetic transition have a metamagnetic behavior with magnetization plateaus at $m/{m}_{\mathrm{sat}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ and $1/2$. The MSE has been proposed to describe solid ${}^{3}\mathrm{He}$ films adsorbed onto graphite, thus we compute the MSE heat capacity for parameters in the low density range of the 2nd layer and find a double-peak structure.