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

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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 system.
Lingua originaleEnglish
pagine (da-a)1274-1287
Numero di pagine14
RivistaJournal of Statistical Physics
Volume146
Stato di pubblicazionePublished - 2012

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Statistical Physics
Central limit theorem
theorems
physics
Criticality
Temperature Dependence
Free Energy
free energy
temperature dependence
temperature
Prediction
predictions

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cita questo

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title = "On the Merit of a Central Limit Theorem-based Approximation in Statistical 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 system.",
keywords = "Quantum statistical mechanics; Central Limit Theorem; Free energy; Ising model",
author = "Antonino Messina and Bruno Leggio and Lychkovskiy",
year = "2012",
language = "English",
volume = "146",
pages = "1274--1287",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",

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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 -