Abstract:
Ground States for Large Samples of Two-dimensional Ising Spin Glasses
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We have developed a combinatoric matching method to find the exact
groundstate energy for the 2D Ising spin glass with the
+J/-J distribution
and equal numbers of positive and negative spins.
For the largest size
(1800 × 1800 plaquettes of spins)
we averaged results from 278 samples
and for the smaller ones from up to 374,375 samples.
We also studied the behavior
of the distributions of computer time (cpu) and memory
as functions of sample size.
We present finite size scaling leading to a groundstate energy estimate of
E = -1.40193 +/- 2 for the infinite system. We found that the memory scales
as the square of sample length and that for a given size,
the CPU time appears to have a skewed and high tailed distribution.
Accepted: International Journal of Modern Physics C
Last Updated: 04-Oct-98