The quantum crossover behaviour of the order parameter of the X- Y model in a transverse magnetic field

Abstract

The quantum crossover behaviour of the order parameter of the d-dimensional (2 < d < 4) X- Y ferromagnet in a transverse field Γ is investigated. The crossover scaling form M = | h| β q φ( z) of the order parameter is obtained, where β q , z a φ( z) denote, respectively, the quantum order parameter exponent, the crossover scaling variable and the scaling function. The calculation of effective exponent β eff as a function of z has been performed.