On the merit of a Central Limit Theorem-based approximation in statistical physics
Statistical Mechanics
2012-03-21 v1 Quantum Physics
Abstract
The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved as well as its inadequacy to disclose quantum criticalities at fixed temperatures. Its high temperature predictions are in addition shown to coincide with those stemming from straightforward appropriate expansions up to (k_B T)^(-2). Our results are clearly illustrated by comparing the exact and approximate temperature dependence of the free energy of some exemplary physical systems.
Cite
@article{arxiv.1111.1091,
title = {On the merit of a Central Limit Theorem-based approximation in statistical physics},
author = {Bruno Leggio and Oleg Lychkovskiy and Antonino Messina},
journal= {arXiv preprint arXiv:1111.1091},
year = {2012}
}
Comments
12 pages, 1 figure