### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 1274-1287 |

Numero di pagine | 14 |

Rivista | Journal of Statistical Physics |

Volume | 146 |

Stato di pubblicazione | Published - 2012 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cita questo

*Journal of Statistical Physics*,

*146*, 1274-1287.

**On the Merit of a Central Limit Theorem-based
Approximation in Statistical Physics.** / Messina, Antonino; Leggio, Bruno; Lychkovskiy.

Risultato della ricerca: Article

*Journal of Statistical Physics*, vol. 146, pagg. 1274-1287.

}

TY - JOUR

T1 - On the Merit of a Central Limit Theorem-based Approximation in Statistical Physics

AU - Messina, Antonino

AU - Leggio, Bruno

AU - Lychkovskiy, null

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Quantum statistical mechanics; Central Limit Theorem; Free energy; Ising model

UR - http://hdl.handle.net/10447/62437

M3 - Article

VL - 146

SP - 1274

EP - 1287

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -