Order by disorder and Kosterlitz-Thouless transitions in classical Gamma-model subject to a magnetic field

We present a combined analytical and numerical study of honeycomb Gamma model subject to magnetic field in the high-symmetry direction. Extensive Monte Carlo simulations are used to obtain the field H versus temperature T phase diagram. We show that the novel plaquette-ordered spin liquid remains stable at low temperatures up to a field H_c1 ≈ 0.5Γ, where Γ is the energy scale of anisotropic exchange interaction. We argue that the stability of this plaquette spin liquid comes from the extensive configurational entropy of hexagonal fluxes. As temperature is lowered, a long-range magnetic order with tripled unit cell is favored energetically. This magnetic ordered ground state gradually transforms to the fully polarized state at an upper critical field of H_c2 = 4Γ. Interestingly, this √3 ×√3 spin order is shown to exhibit an emergent accidental O(2) symmetry, reminiscent of the O(3) rotation symmetry of the zero-field case. We show that a similar thermal order-by-disorder lifts this accidental degeneracy and selects a six-fold degenerate magnetic ground state.For intermediate magnetic field H_c1 < H < H_c2 , the system undergoes two Kosterlitz-Thouless transitions, with an intermediate critical phase, into the √3 ×√3 ground state.