Eur. Phys. J. B (2017) 90: 173
https://doi.org/10.1140/epjb/e2017-80286-1

Regular Article

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

^a e-mail: nisiyama@psun.phys.okayama-u.ac.jp

Received: 21 May 2017
Received in final form: 25 June 2017
Published online: 18 September 2017

Abstract

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ_s in the ordered phase and the vortex-condensate stiffness ρ_v 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 ρ_s,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ_s/ρ_v admits a quantitative measure of deviation from selfduality.