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.
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Notes
The third low can be violated only for systems whose ground state degeneracy grows exponentially with the number of blocks.
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Acknowledgements
OL acknowledges the partial support from grants NSh-4172.2010.2, RFBR-11-02-00778, RFBR-10-02-01398 and from the Ministry of Education and Science of the Russian Federation under contracts No. 02.740.11.0239.
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Leggio, B., Lychkovskiy, O. & Messina, A. On the Merit of a Central Limit Theorem-based Approximation in Statistical Physics. J Stat Phys 146, 1274–1287 (2012). https://doi.org/10.1007/s10955-012-0442-9
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DOI: https://doi.org/10.1007/s10955-012-0442-9