Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-03-20
Europhys.Lett. 67 (2004) 453-459
Physics
Condensed Matter
Disordered Systems and Neural Networks
7 pages, LaTex, 7 ps-figures included, added result for stiffness in d=7, as to appear in Europhysics Letters (see http://ww
Scientific paper
10.1209/epl/i2004-10082-0
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 $y_3=0.24(1)$ for $d=3$, significantly improving on previous work. The results for $d=6$ and $d=7$, $y_6=1.1(1)$ and $y_7=1.24(5)$, are entirely new and are compared with mean-field predictions made for d>=6.
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