Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study

R. R. P. Singh and A. P. Young
Phys. Rev. E 96, 022139 – Published 17 August 2017
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Abstract

We study the ±J transverse-field Ising spin-glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d=6, which is below the upper critical dimension of d=8. In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

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  • Received 5 July 2017
  • Corrected 6 October 2017

DOI:https://doi.org/10.1103/PhysRevE.96.022139

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Corrections

6 October 2017

Erratum

Authors & Affiliations

R. R. P. Singh

  • Department of Physics, University of California, Davis, Davis, California 95616, USA

A. P. Young*

  • Department of Physics, University of California, Santa Cruz, Santa Cruz, California 95064, USA

  • *petery@ucsc.edu

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Issue

Vol. 96, Iss. 2 — August 2017

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