Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

Details Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

1998-12-29

arxiv.org/abs/cond-mat/9812414v1

Phys. Rev. Lett. 81, 5916 (1998)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages RevTeX, 3 eps-figures included

Scientific paper

10.1103/PhysRevLett.81.5916

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension. At the critical point, the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single, continuously varying exponent, z', which diverges at the critical point, as in one-dimension. Consequently, the zero temperature susceptibility diverges for a RANGE of parameters about the transition.

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