2006/07/31 by Ronald Fisch · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Random Matrices and Applications #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-007-9336-7
published as J. Stat. Phys. 128, 1113 (2007) · 13 pages, 7 figures; final version, to appear in J. Stat. Phys
arxiv created 2007/05/15 · openalex publication_date 2007/05/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for L × L square lattices with L ≤ 48, and p = 0.5, where p is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of L, in order to obtain the low temperature behavior of the model. For large finite L there is a range of T in which the heat capacity is proportional to T5.33 ± 0.12. The range of T in which this behavior occurs scales slowly to T = 0 as L increases. Similar results are found for p = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation d ν= 2 - α, even though Tc = 0. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented.