2005/02/28 by Ronald Fisch, R. Fisch · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Condensed matter physics #Configuration entropy #Entropy (arrow of time) #Geometry #Ground state #Ising model #Mathematics #Physics #Quantum mechanics #Residual entropy #Scaling #Spin glass #Statistical physics #Theoretical and Computational Physics #Thermodynamics #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-006-9164-1
published in Journal of Statistical Physics 125(3), 777-792 (Springer Science+Business Media) · 9 pages, two-column format; to appear in J. Statistical Physics
arxiv created 2006/06/23 · openalex publication_date 2006/07/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 L1.78(2). Anomalous scaling is not found for the characteristic energy, which essentially scales as L2. When x= 0.25, a crossover to L2 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.