First-order phase transitions in spinor Bose gases and frustrated magnets
Résumé
We show that phase transitions in spin-1 Bose gases and stacked triangular Heisenberg antiferromagnets—an example of frustrated magnets with competing interactions—are described by the same Landau-Ginzburg-Wilson Hamiltonian with O(3)×O(2) symmetry. In agreement with previous nonperturbative-renormalization-group studies of the three-dimensional O(3)×O(2) model, we find that the transition from the normal phase to the superfluid ferromagnetic phase in a spin-1 Bose gas is weakly first order and shows pseudoscaling behavior. The (nonuniversal) pseudoscaling exponent ν is fully determined by the scattering lengths a0 and a2. We provide estimates of ν in Rb87,K41, and Li7 atom gases which can be tested experimentally. We argue that pseudoscaling comes from either a crossover phenomenon due to proximity of the O(6) Wilson-Fisher fixed point (Rb87 and K41) or the existence of two unphysical fixed points (with complex coordinates) which slow down the RG flow (Li7). These unphysical fixed points are a remnant of the chiral and antichiral fixed points that exist in the O(N)×O(2) model when N is larger than Nc≃5.3 (the transition being then second order and controlled by the chiral fixed point). Finally, we discuss a O(2)×O(2) lattice model and show that our results, even though we find the transition to be first order, are compatible with Monte Carlo simulations yielding an apparent second-order transition.