Simulating frustrated magnetism with spinor Bose gases

Although there is a broad consensus on the fact that critical behavior in stacked triangular Heisenberg antiferromagnets --an example of frustrated magnets with competing interactions-- is described by a Landau-Ginzburg-Wilson Hamiltonian with O(3)$\times$O(2) symmetry, the nature of the phase transition in three dimensions is still debated. We show that spin-one Bose gases provide us with a simulator of the O(3)$\times$O(2) model. Using a renormalization-group approach, we argue that the transition is weakly first order and shows pseudoscaling behavior, and give estimates of the pseudocritical exponent $\nu$ in ${}^{87}$Rb, ${}^{41}$K and ${}^7$Li atom gases which can be tested experimentally.