1999/11/03 by Francisco A. Tamarit, Francisco Tamarit, Celia Anteneodo · 6 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.84.208
4 pages, 4 figures, to appear in Phys. Rev. Lett
arxiv created 1999/11/03 · openalex publication_date 2000/01/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We analyze the equilibrium properties of a chain of ferromagnetically coupled rotators which interact through a force that decays as r^\ensuremath-\ensuremathα where r is the interparticle distance and \ensuremathα\ensuremath≥0. By integrating the equations of motion we obtain the microcanonical time averages of both the magnetization and the kinetic energy. We detect three different regimes depending on whether \ensuremathα belongs to the intervals [0,1), (1,2), or (2,\ensuremath∞). For 0<\ensuremathα<1, the microcanonical averages agree, after a scaling, with those obtained in the canonical ensemble for the mean-field case (\ensuremathα\phantom\rule0ex0ex=\phantom\rule0ex0ex0). This correspondence offers a mathematically tractable way of dealing with systems governed by slowly decaying long-range interactions.