Duality - mediated critical amplitude ratios for the ( 2 + 1 ) - dimensional S = 1 XY model

The phase transition for the (2 + 1)-dimensional spin-S = 1 XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortexcondensate stiffness ρv in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρs,v/∆ (∆: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρs/ρv admits a quantitative measure of deviation from selfduality. PACS. 75.10.Jm Quantized spin models – 05.70.Jk Critical point phenomena – 75.40.Mg Numerical simulation studies – 05.50.+q Lattice theory and statistics (Ising, Potts, etc.)