1997/07/31 by M. E. J. Newman, Cristopher Moore · 133 citations
Materials Science · Mathematics · Physics and Astronomy · #Annealing (glass) #Complex Network Analysis Techniques #Condensed matter physics #Distribution function #Hamiltonian (control theory) #Material Dynamics and Properties #Mathematics #Measure (data warehouse) #Partition function (quantum field theory) #Physics #Quantum mechanics #Randomness #Spin glass #Spin model #Statistical physics #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.60.5068
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 60(5), 5068-5072 (American Physical Society) · 16 pages, 4 postscript figures, typeset in LaTeX using the RevTeX macro package
arxiv created 1999/08/24 · openalex publication_date 1999/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a simple two-dimensional spin model with short-range interactions which shows glassy behavior despite a Hamiltonian which is completely homogeneous and possesses no randomness. We solve exactly for both the static partition function of the model and the distribution of energy barriers, giving us the equilibration time scales at low temperature. Simulations of instantaneous quenches and of annealing of the model are in good agreement with the analytic calculations. We also measure the two-time spin correlation as a function of waiting time, and show that the model has aging behavior consistent with the distribution of barrier heights. The model appears to have no sharp glass transition. Instead, it falls out of equilibrium at a temperature which decreases logarithmically as a function of the cooling time.