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Physics Letters A

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

K. Lukierska‐Walasek

Published Jul 1, 1985• 0 citations
Publisher
DOI
10.1016/0375-9601(85)90764-9

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The field theoretical renormalisation group method, which correctly describes the critical as well as the multicritical (at zero temperature) behaviours of the quantum mechanical d-dimensional Ising model in a transverse magnetic field, is proposed. Due to the introduction of the additional renormalisation the singularities associated with zero temperature have been removed. The crossover scaling form of the inverse correlation length and longitudinal susceptibility are considered for the following spatial dimensions d:2<d<3, d=3 and 3<d<4. For 2<d<3, d=3 and 3<d<4 the calculations are performed to the first order in 3-d and 4-d, respectively.
Ten terms have been obtained in the high-temperature series for the fluctuation in long-range order of the Ising model in a transverse magnetic field on the three cubic lattices. This model is relevant to real materials such as singlet-singlet magnetic systems, hydrogen-bonded ferroelectrics and cooperative Jahn-Teller systems. The critical temperature of the system was obtained over essentially the entire range of the transverse field for which a phase transition exists. No crossover to the expected d=4 critical behaviour was observed at T=0.