Abstract
We study a Hamiltonian of S = 1/2 spins with two-, three and four-spin exchange interactions on the triangular lattice as a possible model of the nuclear magnetism of solid 3 He layers. The spin wave theory shows that the “tetrahedral” ground state, which was shown to be favoured by the four-spin exchange interaction in our previous paper, is stable against quantum fluctuations in some parameter region. Since this state has a scalar chiral long-range order, a phase transition occurs at a finite temperature even though the Hamiltonian has a full rotational symmetry in the spin space. Critical behavior of this phase transition was examined by classical Monte Carlo simulations. The specific heat diverges much more strongly than that of the 2D Ising model.
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Kubo, K., Momoi, T. & Niki, K. Possibility of a Chiral Phase Transition in Two-Dimensional 3He Solid. Journal of Low Temperature Physics 110, 339–344 (1998). https://doi.org/10.1023/A:1022592918545
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DOI: https://doi.org/10.1023/A:1022592918545