Octupolar order in the multiple spin exchange model on a triangular lattice

We showed how a gapless spin liquid with hidden octupolar order arises in applied magnetic field, in a model applicable to thin films of solid $^3$He with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. In this, dynamical effects lead to the formation of three-magnon bound states, which undergo Bose-Einstein condensation, giving rise to octupolar order. We confirmed its existence through the exact diagonalization of finite-size clusters. We also presented evidence for nematic -- i.e. quadrupolar -- correlations bordering on ferromagnetism in the absence of magnetic field.