Quantum effects in the critical properties of the X-Y model in a transverse magnetic field: crossover scaling near zero temperature

Abstract

The susceptibility of a quantum X-Y model in a transverse field Gamma is studied in the vicinity of the multicritical point ( Gamma c,T=0). For dimensions d between two and four we obtain a Hartree type approximation an equation for the corresponding crossover function which is solvable analytically in three dimensions. The critical line Gamma c(T)- Gamma c(0) approximately Tpsi is asymptotically described by the shift exponent psi =d/2 in accord with self-consistent spin wave theory. For the variable of the crossover scaling function T/( Gamma - Gamma c(T))phi one obtains the crossover exponent phi =(4-d)/2 which is characteristic for the Gaussian multicritical point. A dimensional-analysis argument suggests that this is valid beyond the approximation.