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Journal of Physics A Mathematical and General

Phase transitions in the random field Ising model in the presence of a transverse field

Amit Dutta, Bikas K. Chakrabarti, Robin B. Stinchcombe

Published Sep 7, 1996• 12 citations
Publisher

Abstract

We have studied the phase transition behaviour of the random field Ising model in the presence of a transverse (or tunnelling) field. The mean field phase diagram has been studied in detail, and in particular the nature of the transition induced by the tunnelling (transverse) field at zero temperature. A modified hyperscaling relation for the zero-temperature transition has been derived using the Suzuki - Trotter formalism and a modified `Harris criterion'. A mapping of the model to a randomly diluted antiferromagnetic Ising model in uniform longitudinal and transverse field is also given.

DOI
10.1088/0305-4470/29/17/007

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Physical review. B, Condensed matter•Jun 1, 1991•25 citations
We have studied the phase transition behaviour of the random field Ising model in the presence of a transverse (or tunnelling) field. The mean field phase diagram has been studied in detail, and in particular the nature of the transition induced by the tunnelling (transverse) field at zero temperature. A modified hyperscaling relation for the zero-temperature transition has been derived using the Suzuki - Trotter formalism and a modified `Harris criterion'. A mapping of the model to a randomly diluted antiferromagnetic Ising model in uniform longitudinal and transverse field is also given.
The effect of random bond (site) dilution on the phase transition of a three-dimensional transverse Ising model is studied by a cluster variation, along with perturbation expansion method. Complete phase diagrams in the temperature-concentration-transverse-field space are constructed for both the cases. The value of critical transverse field as a function of concentration, at zero temperature, exhibits a discontinuity at the critical value of concentration for the existence of phase transition, as conjectured by Harris. As is expected for the existence of a second-order phase transition, the static susceptibility diverges on the critical surface.
We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension d>2d>2d>2, there is at low strength of randomness and transverse field a phase with true long-range order that is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite-temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e., the logarithm of the diverging time scale rises as a power of the diverging length scale.
We determine the phase diagram of the transverse Ising model with a trimodal distribution (sum of three \ensuremath{\delta} functions) for a longitudinal random field at T=0, using a mean-field approximation. The phase diagram includes tricritical points, ordered critical points, a fourth-order point, critical end points, and a double critical end point. Our T=0 phase diagram is completely equivalent to the one obtained by Kaufman, Klunzinger, and Khurana for the random-field Ising model. We show that the temperature and the magnitude of the transverse field play a similar role.