Europhys. Lett.
Volume 67, Number 3, August 2004
Page(s) 453 - 459
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 01 July 2004
Europhys. Lett., 67 (3), pp. 453-459 (2004)
DOI: 10.1209/epl/i2004-10082-0

Low-temperature excitations of dilute lattice spin glasses

S. Boettcher

Physics Department, Emory University - Atlanta, Georgia 30322, USA

(Received 12 January 2004; accepted in final form 26 May 2004)

A new approach to exploring low-temperature excitations in finite-dimensional lattice spin glasses is proposed. By focusing on bond-diluted lattices just above the percolation threshold, large system sizes L can be obtained which lead to enhanced scaling regimes and more accurate exponents. Furthermore, this method in principle remains practical for any dimension, yielding exponents that so far have been elusive. This approach is demonstrated by determining the stiffness exponent for dimensions d=3, d=6 (the upper critical dimension), and d=7. Key is the application of an exact reduction algorithm, which eliminates a large fraction of spins, so that the reduced lattices never exceed $\sim10^3$ variables for sizes as large as L=30 in d=3, L=9 in d=6, or L=8 in d=7. Finite-size scaling analysis gives y3=0.24(1) for d=3, significantly improving on previous work. The results for d=6 and d=7, y6=1.1(1) and y7=1.24(5), are entirely new and are compared with mean-field predictions made for $d\geq 6$.

75.10.Nr - Spin-glass and other random models.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
02.60.Pn - Numerical optimization.

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