Effective spin-glass Hamiltonian for the anomalous dynamics of the HMF model

2005/06/30 by Alessandro Pluchino, Vito Latora, Andrea Rapisarda
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physa.2006.03.067

published as Physica A 370 (2006) 573 · Revtex, 9 pages, 2 figures. New revised version revised according to the referee reports

arxiv created 2006/02/06 · openalex publication_date 2006/07/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss an effective spin-glass Hamiltonian which can be used to study the glassy-like dynamics observed in the metastable states of the Hamiltonian Mean Field (HMF) model. By means of the Replica formalism, we were able to find a self-consistent equation for the glassy order parameter which reproduces, in a restricted energy region below the phase transition, the microcanonical simulations for the polarization order parameter recently introducted in the HMF model.

Citations

• Rotators with Long-Range Interactions: Connection with the Mean-Field Approximation
• Solution of 'Solvable model of a spin glass'
• Vlasov stability of the Hamiltonian mean field model