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Physica B+C

Critical behaviour of the Ising model in a transverse field

J. Oitmaa, Michael Plischke

Published Jan 1, 1977• 8 citations
Publisher
DOI
10.1016/0378-4363(77)90602-7

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The critical behaviour of the susceptibility of the Ising model with a transverse field is investigated by means of the perturbation expansions. Exact expressions for the coefficients up to seventh order in J / k T are given as functions of Δ/ k T for the quadratic, triangular, simple cubic, b.c.c. and f.c.c. lattices. The universality of the critical index is concluded from the analysis of the coefficients and the critical temperature is obtained as function of the transverse field for the five kinds of lattices.

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The quantum-classical crossover critical behaviour of the Ising model in a transverse field

Pierre M. Pfeuty

The quantum-classical crossover critical behaviour of the Ising model in a transverse field Gamma is first studied in one dimension where exact results are obtained. The correspondence between the quantum-classical crossover behaviour of this d-dimensional quantum model and the finite-size crossover behaviour of an equivalent (d+1)-dimensional classical model exact for d=1 is extended to higher dimensions. The crossover depends strongly on the relative magnitude of the crossover exponent phi and of the critical line-shift exponent Psi . In particular, if Pi > Psi approaches the critical line along a path of constant transverse field less than the critical field Gamma c and a low temperature, only classical behaviour is seen, quantum effects do not show up. There is some controversy about the value of Psi . Experiments are suggested to give an answer.

Journal of Physics C Solid State Physics•Nov 14, 1976•52 citations
The critical behaviour of the susceptibility of the Ising model with a transverse field is investigated by means of the perturbation expansions. Exact expressions for the coefficients up to seventh order in J / k T are given as functions of Δ/ k T for the quadratic, triangular, simple cubic, b.c.c. and f.c.c. lattices. The universality of the critical index is concluded from the analysis of the coefficients and the critical temperature is obtained as function of the transverse field for the five kinds of lattices.
The quantum-classical crossover critical behaviour of the Ising model in a transverse field Gamma is first studied in one dimension where exact results are obtained. The correspondence between the quantum-classical crossover behaviour of this d-dimensional quantum model and the finite-size crossover behaviour of an equivalent (d+1)-dimensional classical model exact for d=1 is extended to higher dimensions. The crossover depends strongly on the relative magnitude of the crossover exponent phi and of the critical line-shift exponent Psi . In particular, if Pi > Psi approaches the critical line along a path of constant transverse field less than the critical field Gamma c and a low temperature, only classical behaviour is seen, quantum effects do not show up. There is some controversy about the value of Psi . Experiments are suggested to give an answer.