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The Parisi Formula has a Unique Minimizer
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...
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| Published in: | Communications in mathematical physics 2015-05, Vol.335 (3), p.1429-1444 |
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| container_issue | 3 |
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| container_title | Communications in mathematical physics |
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| creator | Auffinger, Antonio Chen, Wei-Kuo |
| description | 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. |
| doi_str_mv | 10.1007/s00220-014-2254-z |
| format | article |
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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.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-014-2254-z</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Classical and Quantum Gravitation ; Complex Systems ; Mathematical and Computational Physics ; Mathematical Physics ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Communications in mathematical physics, 2015-05, Vol.335 (3), p.1429-1444</ispartof><rights>Springer-Verlag Berlin Heidelberg 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-3213652c0e1ce0a7b3f2659c3c2af319e7dea76c4008eaeb891be0df70481a003</citedby><cites>FETCH-LOGICAL-c358t-3213652c0e1ce0a7b3f2659c3c2af319e7dea76c4008eaeb891be0df70481a003</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>Auffinger, Antonio</creatorcontrib><creatorcontrib>Chen, Wei-Kuo</creatorcontrib><title>The Parisi Formula has a Unique Minimizer</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>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.</description><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9j7FOwzAURS0EEqHwAWxeGQzv2YmTjKiiFKmoHdrZctwX6qpJwCYD-XpShZnpLvdc3cPYPcIjAuRPEUBKEICpkDJLxXDBEkyVFFCivmQJAIJQGvU1u4nxCACl1DphD9sD8Y0NPnq-6ELTnyw_2Mgt37X-qyf-7lvf-IHCLbuq7SnS3V_O2G7xsp0vxWr9-jZ_XgmnsuJbKIlKZ9IBoSOweaVqqbPSKSdtrbCkfE821y4FKMhSVZRYEezrHNICLYCaMZx2XehiDFSbz-AbG34Mgjm7msnVjK7m7GqGkZETE8du-0HBHLs-tOPNf6BfOitWCA</recordid><startdate>20150501</startdate><enddate>20150501</enddate><creator>Auffinger, Antonio</creator><creator>Chen, Wei-Kuo</creator><general>Springer Berlin Heidelberg</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150501</creationdate><title>The Parisi Formula has a Unique Minimizer</title><author>Auffinger, Antonio ; Chen, Wei-Kuo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-3213652c0e1ce0a7b3f2659c3c2af319e7dea76c4008eaeb891be0df70481a003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Auffinger, Antonio</creatorcontrib><creatorcontrib>Chen, Wei-Kuo</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Auffinger, Antonio</au><au>Chen, Wei-Kuo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Parisi Formula has a Unique Minimizer</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2015-05-01</date><risdate>2015</risdate><volume>335</volume><issue>3</issue><spage>1429</spage><epage>1444</epage><pages>1429-1444</pages><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>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.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-014-2254-z</doi><tpages>16</tpages></addata></record> |
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| source | Springer Nature |
| subjects | Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical |
| title | The Parisi Formula has a Unique Minimizer |
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