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Physics Letters A

On the zero-temperature critical behaviour of the quantum X-Y model in a transverse magnetic field

T. K. Kopeć, G. KozĐowski

Published Apr 1, 1983• 19 citations
Publisher
DOI
10.1016/0375-9601(83)90151-2

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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.
The zero-temperature critical behaviours of the classical Heisenberg and XY ferromagnets in the uniaxial random field are studied in the arbitrary spatial dimension. Exact results are obtained for the magnetization, transversal to the random field direction, at the Gaussian and bimodal distributions of the random field. For the Gaussian distribution the critical behaviour in strong random fields is independent of the spatial dimension. The transversal magnetization, , where is the distribution width. For the bimodal distribution of the random field, the transversal magnetization obeys the law , where is a critical field, and H is the random field amplitude. The same critical behaviour is expected for related systems, for example random antiferromagnets in the uniform field.