Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model
Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan
Received: 21 May 2017
Received in final form: 25 June 2017
Published online: 18 September 2017
The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortex-condensate 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/Δ (Δ: 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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2017