Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
979736 | Physica A: Statistical Mechanics and its Applications | 2006 | 12 Pages |
Abstract
We study the mean-field Ï4 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 Nââ 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 Nââ values as N is increased. As expected, finite size effects scale as N-1.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Alessandro Campa, Stefano Ruffo,