TY - JOUR
T1 - The Parisi Formula has a Unique Minimizer
AU - Auffinger, Antonio
AU - Chen, Wei Kuo
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2015/5
Y1 - 2015/5
N2 - In 1979, Parisi (Phys Rev Lett 43:1754–1756, 1979) predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington–Kirkpatrick model, and described the role played by its minimizer. This formula was verified in the seminal work of Talagrand (Ann Math 163(1):221–263, 2006) and later generalized to the mixed p-spin models by Panchenko (Ann Probab 42(3):946–958, 2014). In this paper, we prove that the minimizer in Parisi’s formula is unique at any temperature and external field by establishing the strict convexity of the Parisi functional.
AB - In 1979, Parisi (Phys Rev Lett 43:1754–1756, 1979) predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington–Kirkpatrick model, and described the role played by its minimizer. This formula was verified in the seminal work of Talagrand (Ann Math 163(1):221–263, 2006) and later generalized to the mixed p-spin models by Panchenko (Ann Probab 42(3):946–958, 2014). In this paper, we prove that the minimizer in Parisi’s formula is unique at any temperature and external field by establishing the strict convexity of the Parisi functional.
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U2 - 10.1007/s00220-014-2254-z
DO - 10.1007/s00220-014-2254-z
M3 - Article
AN - SCOPUS:84925538338
SN - 0010-3616
VL - 335
SP - 1429
EP - 1444
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -