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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Kluwer Academic Publishers-Plenum Publishers

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DOI

10.1016/0038-1101(64)90047-4

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1572-9613

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FiniteSize Scaling in the EnergyEntropy Plane fo

Authors: Ronald Fisch
Publish Date: 2006/07/26
Volume: 125, Issue: 3, Pages: 777-792
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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=05 where x is the fraction of negative bonds over this range of L the characteristic entropy defined by the energyentropy correlation scales with size as L 1782 Anomalous scaling is not found for the characteristic energy which essentially scales as L 2 When x=025 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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Other Papers In This Journal:
  1. Mean Field Dilute Ferromagnet: High Temperature and Zero Temperature Behavior
  2. Probabilistic Cellular Automata for Low-Temperature 2-d Ising Model
  3. Random Birth-and-Death Networks
  4. Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma
  5. On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices
  6. Products of Random Matrices and Generalised Quantum Point Scatterers
  7. Symmetry of the Linearized Boltzmann Equation and Its Application
  8. Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov
  9. Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity
  10. Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System
  11. Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties
  12. New Horizons in Multidimensional Diffusion: The Lorentz Gas and the Riemann Hypothesis
  13. Clustering of Fermionic Truncated Expectation Values Via Functional Integration
  14. Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry–Mather Theory
  15. Revisiting the Glansdorff–Prigogine Criterion for Stability Within Irreversible Thermodynamics
  16. Ground State Energy of the One-Dimensional Discrete Random Schrödinger Operator with Bernoulli Potential
  17. A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths
  18. The More the Merrier?
  19. Non-equilibrium Phase Diagram for a Model with Coalescence, Evaporation and Deposition
  20. Real Spin Glasses Relax Slowly in the Shade of Hierarchical Trees
  21. Galton–Watson Trees with Vanishing Martingale Limit
  22. A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings
  23. Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians
  24. Dynamics of Infinitely Many Particles Mutually Interacting in Three Dimensions via a Bounded Superstable Long-Range Potential
  25. Statistical Mechanics of Nucleosomes Constrained by Higher-Order Chromatin Structure
  26. Large Deviations for the Branching Brownian Motion in Presence of Selection or Coalescence
  27. Clustering Bounds on n -Point Correlations for Unbounded Spin Systems
  28. Dissipative Diamagnetism—A Case Study for Equilibrium and Nonequilibrium Statistical Mechanics
  29. On the Transfer of Energy Towards Infinity in the Theory of Weak Turbulence for the Nonlinear Schrödinger Equation
  30. Finite-Time Fluctuations in the Degree Statistics of Growing Networks
  31. Exotic Ground States of Directional Pair Potentials via Collective-Density Variables
  32. Strong Asymmetric Coupling of Two Parallel Exclusion Processes
  33. Repeated Interaction Quantum Systems: Van Hove Limits and Asymptotic States
  34. On the Dynamics of the Glass Transition on Bethe Lattices
  35. Coarsening Dynamics on $$\mathbb {Z}^d$$ with Frozen Vertices
  36. A Class of Random Walks in Reversible Dynamic Environments: Antisymmetry and Applications to the East Model
  37. Power-law Decay and the Ergodic–Nonergodic Transition in Simple Fluids
  38. Rigorous Treatment of the Liquid-Vapor Transition in a Polydisperse System with Kac Interaction
  39. R -Local Delaunay Inhibition Model
  40. Patterns and Symmetries in the Visual Cortex and in Natural Images
  41. Parameter Estimation for Multiscale Diffusions
  42. Onsager and Kaufman’s Calculation of the Spontaneous Magnetization of the Ising Model: II
  43. Injected Power Fluctuations in 1D Dissipative Systems
  44. Anomalies in Conductance and Localization Length of Disordered Ladders
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