A very simple proof of the LSI for high temperature spin systems

A very simple proof of the LSI for high temperature spin systems

We present a very simple proof that the O(n) model satisfies a uniform logarithmic Sobolev inequality (LSI) if the difference between the largest and the smallest eigenvalue of the coupling matrix is less than n. This condition applies in particular to the SK spin glass model at inverse temperature...

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Veröffentlicht in:Journal of functional analysis 2019-04, Vol.276 (8), p.2582-2588
Hauptverfasser: Bauerschmidt, Roland, Bodineau, Thierry
Format: Artikel
Sprache:eng
Schlagworte:
Logarithmic Sobolev inequality
Mathematical Physics
Mathematics
Physics
Probability
Spin glasses
Spin systems
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Zusammenfassung:We present a very simple proof that the O(n) model satisfies a uniform logarithmic Sobolev inequality (LSI) if the difference between the largest and the smallest eigenvalue of the coupling matrix is less than n. This condition applies in particular to the SK spin glass model at inverse temperature β
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2019.01.007