Abstract
For L × L square lattices with L ≤ 20 the 2D Ising spin glass with +1 and −1 bonds is found to have a strong correlation between the energy and the entropy of its ground states. A fit to the data gives the result that each additional broken bond in the ground state of a particular sample of random bonds increases the ground state degeneracy by approximately a factor of 10/3. For x=0.5 (where x is the fraction of negative bonds), over this range of L, the characteristic entropy defined by the energy-entropy correlation scales with size as L 1.78(2). Anomalous scaling is not found for the characteristic energy, which essentially scales as L 2. When x=0.25, a crossover to L 2 scaling of the entropy is seen near L=12. The results found here suggest a natural mechanism for the unusual behavior of the low temperature specific heat of this model, and illustrate the dangers of extrapolating from small L.
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PACS numbers: 75.10.Nr, 75.40.Mg, 75.50.Lk
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Fisch, R. Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass. J Stat Phys 125, 777–792 (2006). https://doi.org/10.1007/s10955-006-9164-1
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DOI: https://doi.org/10.1007/s10955-006-9164-1