Quantum classical crossover critical behavior of the Ising model in a transverse field

Kristoffer Aronsen

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.

Zvi Friedman

Critical indices, the critical line, and the crossover scaling function for the free energy are calculated for the two-dimensional Ising model with a transverse field using a quantum-mechanical version of the real-space renormalization group. The critical behavior as function of the transverse field at a small finite temperature changes from that of a three-dimensional to that of a two-dimensional Ising behavior, as the critical line is approached.

Julia Mihailowa Wesselinowa

J. Oitmaa, Michael Plischke

J. Oitmaa, G J Coombs

The authors have investigated the properties of the Ising model in a transverse field for general spin S by the method of high-temperature series. Analysis of the series yields the form of the phase diagram in the temperature field plane. The authors also investigate the variation of critical field with spin, and present evidence for classical-quantum crossover at T=0 for all spin values.