2005/09/01 by Alessandro Campa, Stefano Ruffo
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Field (mathematics) #Gaussian Processes and Bayesian Inference #Mathematics #Physics #Pure mathematics #Statistical Mechanics and Entropy #Statistical physics #Statistics #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2006.01.066
published as Physica A369 (2006) 517-528 · 18 pages, 1 figure
arxiv created 2005/09/01 · openalex publication_date 2006/02/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We solve the mean-field ϕ4 model in an external magnetic field in the microcanonical ensemble using two different methods. The first one is based on Rugh's microcanonical formalism and leads to express macroscopic observables, such as temperature, specific heat, magnetization and susceptibility, as time averages of convenient functions of the phase-space. The approach is applicable for any finite number of particles N. The second method uses large deviation techniques and allows us to derive explicit expressions for microcanonical entropy and for macroscopic observables in the N →∞ limit. Assuming ergodicity, we evaluate time averages in molecular dynamics simulations and, using Rugh's approach, we determine the value of macroscopic observables at finite N. These averages are affected by a slow time evolution, often observed in systems with long-range interactions. We then show how the finite N time averages of macroscopic observables converge to their corresponding N→∞ values as N is increased. As expected, finite size effects scale as N-1.