Properties of the random field Ising model in a transverse magnetic field

Details Properties of the random field Ising model in a transverse magnetic field Properties of the random field Ising model in a transverse magnetic field

1997-09-15

arxiv.org/abs/cond-mat/9709164v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevB.57.8375

We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension $d > 2$, there is at low strength of randomness and transverse field, a phase with true long range order which 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.

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