The order parameter and quantum crossover in the transverse Ising model

Abstract

It has been shown that in the quantum crossover region, the order parameter of the transverse Ising model can be represented as M ̃ = |h| βqΦ(z) with z ∼ T| h| − ϕ , where h = (Γ − Γ c ) Γ c , β q , ϕ and Φ(z) denote the transverse field deviation, quantum order parameter exponent, crossover exponent, and scaling function, respectively. The equations for Φ( z) in the spatial dimensions 2 < d < 3, d = 3 and 3 < d < 4 have been obtained. The numerical analysis of these equations has been performed yielding the variation of the effective exponent β eff with scaling variable z.