Quantum crossover in the transverse Ising model

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Abstract
The critical behaviour of d dimensional Ising models in a transverse magnetic field, Gamma , is investigated using a quantal generalisation of the Landau-Ginzburg-Wilson free-energy functional introduced by Hertz and Young (1976). A variational approximation of the Hartree type allows a detailed analysis: behaviour near the critical line, Gamma = Gamma c(T) is governed by the exponents of the d dimensional spherical model (which are mean-field-like for d>or=4). However, the point ( Gamma ,T)=( Gamma c(0),0) is multicritical in nature, and characterised by the exponents of the (d+1) dimensional spherical model. Crossover scaling functions, valid near the multicritical point, are found for the longitudinal susceptibility and free energy. They involve the crossover exponent phi T; for 2d+1=1/(d-1); for 32, with the finite-size scaling analogy suggested by Suzuki (1976) and others.

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