On the merit of a Central Limit Theorem-based approximation in statistical physics

Details On the merit of a Central Limit Theorem-based approximation in statistical physics On the merit of a Central Limit Theorem-based approximation in statistical physics

2011-11-04

arxiv.org/abs/1111.1091v1

J Stat Phys (2012) 146:1274-1287

Physics

Condensed Matter

Statistical Mechanics

12 pages, 1 figure

Scientific paper

10.1007/s10955-012-0442-9

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.

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