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Spectral dimensionality of random superconducting networks
Physical Review B (1988)
  • Anthony Roy Day, John Carroll University
  • W. Xia
  • M. F. Thorpe

We compute the spectral dimensionality d-tilde of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d-tilde=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d-tilde=2d/(2-s/ nu ), where s is the superconducting exponent and nu the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d-tilde=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations and the ‘‘termite’’ problem of a random walker on a random superconducting-normal network and point out difficulties in inferring d-tilde from simulations of the termite problem.

Publication Date
Publisher Statement
Published in Physical Review B, Volume 37, Issue 10, 1988, pages 4930-4935. Day, A.R., Xia, W. and Thorpe, M.F. (1988). Spectral dimensionality of random superconducting networks. Physical Review B, 37(10), 4930-4935. doi: 10.1103/PhysRevB.37.4930 © 1988 The American Physical Society.
Citation Information
Anthony Roy Day, W. Xia and M. F. Thorpe. "Spectral dimensionality of random superconducting networks" Physical Review B Vol. 37 Iss. 10 (1988)
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