On the Merit of a Central Limit Theorem-based Approximation in Statistical Physics
- Autori: Leggio, B.; Lychkovskiy, O.; Messina, A.
- Anno di pubblicazione: 2012
- Tipologia: Articolo in rivista (Articolo in rivista)
- Parole Chiave: Quantum statistical mechanics; Central Limit Theorem; Free energy; Ising model
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 system.