Microcanonical solution of the mean-field φ4 model: Comparison with time averages at finite size

Alessandro Campa and Stefano Ruffo

Physica A: Statistical Mechanics and its Applications, 2006, vol. 369, issue 2, 517-528

Abstract: We study 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.

Keywords: Microcanonical ensemble; Mean-field models; Finite size effects (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437106001415
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:369:y:2006:i:2:p:517-528

DOI: 10.1016/j.physa.2006.01.066

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().