O(n) quantum rotors close to n=2 and d=1

Abstract

We investigate the role of topological defects in the zero-temperature transition in an n-component quantum rotor with ferromagnetic interaction on a d-dimensional lattice close to d=1,n=2. The topological defects in the present problem are identified with higher-dimensional classical defects arising in the imaginary time classical action of the quantum rotor. In the same spirit as in Cardy and Hamber [Phys. Rev. Lett. 45, 499 (1980)], we use the analyticity of the renormalization-group equations. In the (d,n) plane, there is a line passing through (1,2) across which the critical exponents are nonanalytic. As expected a clear d?(d+1) correspondence is seen between the quantum and equivalent classical transitions.