Fractal Dimension of Interfaces in Edwards-Anderson and Long-range Ising Spin Glasses: Determining the Applicability of Different Theoretical Descriptions

Wenlong Wang, M. A. Moore, and Helmut G. Katzgraber
Phys. Rev. Lett. 119, 100602 – Published 7 September 2017

Abstract

The fractal dimension of excitations in glassy systems gives information on the critical dimension at which the droplet picture of spin glasses changes to a description based on replica symmetry breaking where the interfaces are space filling. Here, the fractal dimension of domain-wall interfaces is studied using the strong-disorder renormalization group method pioneered by Monthus [Fractals 23, 1550042 (2015)] both for the Edwards-Anderson spin-glass model in up to 8 space dimensions, as well as for the one-dimensional long-ranged Ising spin-glass with power-law interactions. Analyzing the fractal dimension of domain walls, we find that replica symmetry is broken in high-enough space dimensions. Because our results for high-dimensional hypercubic lattices are limited by their small size, we have also studied the behavior of the one-dimensional long-range Ising spin-glass with power-law interactions. For the regime where the power of the decay of the spin-spin interactions with their separation distance corresponds to 6 and higher effective space dimensions, we find again the broken replica symmetry result of space filling excitations. This is not the case for smaller effective space dimensions. These results show that the dimensionality of the spin glass determines which theoretical description is appropriate. Our results will also be of relevance to the Gardner transition of structural glasses.

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  • Received 25 March 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.100602

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Wenlong Wang1,*, M. A. Moore2, and Helmut G. Katzgraber1,3,4

  • 1Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
  • 2School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
  • 31QB Information Technologies (1QBit), Vancouver, British Columbia, Canada V6B 4W4
  • 4Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

  • *wenlongcmp@gmail.com

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Issue

Vol. 119, Iss. 10 — 8 September 2017

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