Ground states for large samples of two-dimensional Ising spin glasses

We have developed a combinatoric matching method to find the exact groundstate energy for the 2-D Ising spin glass with the ±J distribution and equal numbers of positive and negative bonds. For the largest size (1800 × 1800 plaquettes of spins), we averaged results from 278 samples and for the smaller ones 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.

Duke Scholars

Author Richard G. Palmer Physics