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Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph
We consider a gauge symmetric version of the p -spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161, 2001 ) to rigorously compute the free energy. In the c...
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| Published in: | Journal of statistical physics 2009-07, Vol.136 (2), p.205-230 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c288t-c2a0ea8ea55f94bc374da4460955e8dcd8ac6ed36996c24f35a11852ec5afc613 |
| container_end_page | 230 |
| container_issue | 2 |
| container_start_page | 205 |
| container_title | Journal of statistical physics |
| container_volume | 136 |
| creator | Korada, Satish Babu Macris, Nicolas |
| description | We consider a gauge symmetric version of the
p
-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161,
2001
) to rigorously compute the free energy. In the case of pairwise interactions (
p
=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even
p
≥4 except in a range of parameters surrounding the phase transition line, and for odd
p
≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd
p
and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained. |
| doi_str_mv | 10.1007/s10955-009-9781-6 |
| format | article |
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p
-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161,
2001
) to rigorously compute the free energy. In the case of pairwise interactions (
p
=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even
p
≥4 except in a range of parameters surrounding the phase transition line, and for odd
p
≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd
p
and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained.</description><identifier>ISSN: 0022-4715</identifier><identifier>EISSN: 1572-9613</identifier><identifier>DOI: 10.1007/s10955-009-9781-6</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Mathematical and Computational Physics ; Physical Chemistry ; Physics ; Physics and Astronomy ; Quantum Physics ; Statistical Physics and Dynamical Systems ; Theoretical</subject><ispartof>Journal of statistical physics, 2009-07, Vol.136 (2), p.205-230</ispartof><rights>Springer Science+Business Media, LLC 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-c2a0ea8ea55f94bc374da4460955e8dcd8ac6ed36996c24f35a11852ec5afc613</citedby><cites>FETCH-LOGICAL-c288t-c2a0ea8ea55f94bc374da4460955e8dcd8ac6ed36996c24f35a11852ec5afc613</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Korada, Satish Babu</creatorcontrib><creatorcontrib>Macris, Nicolas</creatorcontrib><title>Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph</title><title>Journal of statistical physics</title><addtitle>J Stat Phys</addtitle><description>We consider a gauge symmetric version of the
p
-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161,
2001
) to rigorously compute the free energy. In the case of pairwise interactions (
p
=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even
p
≥4 except in a range of parameters surrounding the phase transition line, and for odd
p
≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd
p
and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained.</description><subject>Mathematical and Computational Physics</subject><subject>Physical Chemistry</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Statistical Physics and Dynamical Systems</subject><subject>Theoretical</subject><issn>0022-4715</issn><issn>1572-9613</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9kEFOwzAQRS0EEqVwAHa-gMF2YsdeoqqUSkUsCmtrcCZtqiSO7FSit8dVWbOZ2fw3mv8IeRT8SXBePSfBrVKMc8tsZQTTV2QmVCWZ1aK4JjPOpWRlJdQtuUvpwHPQWDUjm-UP-IluQ3ec2jDQ0NBpj3QFxx3S7anvcYqtpyPbju1AVx2kRN9DjR3NYaCL0I8dThmIMO7vyU0DXcKHvz0nX6_Lz8Ub23ys1ouXDfPSmClP4AgGQanGlt--qMoaylKfG6CpfW3Aa6wLba32smwKBUIYJdEraHzuMyfictfHkFLExo2x7SGenODurMNddLjc0p11OJ0ZeWFSzg47jO4QjnHIb_4D_QIiD2KM</recordid><startdate>20090701</startdate><enddate>20090701</enddate><creator>Korada, Satish Babu</creator><creator>Macris, Nicolas</creator><general>Springer US</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20090701</creationdate><title>Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph</title><author>Korada, Satish Babu ; Macris, Nicolas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-c2a0ea8ea55f94bc374da4460955e8dcd8ac6ed36996c24f35a11852ec5afc613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Mathematical and Computational Physics</topic><topic>Physical Chemistry</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Statistical Physics and Dynamical Systems</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Korada, Satish Babu</creatorcontrib><creatorcontrib>Macris, Nicolas</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of statistical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Korada, Satish Babu</au><au>Macris, Nicolas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph</atitle><jtitle>Journal of statistical physics</jtitle><stitle>J Stat Phys</stitle><date>2009-07-01</date><risdate>2009</risdate><volume>136</volume><issue>2</issue><spage>205</spage><epage>230</epage><pages>205-230</pages><issn>0022-4715</issn><eissn>1572-9613</eissn><abstract>We consider a gauge symmetric version of the
p
-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161,
2001
) to rigorously compute the free energy. In the case of pairwise interactions (
p
=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even
p
≥4 except in a range of parameters surrounding the phase transition line, and for odd
p
≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd
p
and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10955-009-9781-6</doi><tpages>26</tpages></addata></record> |
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| subjects | Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| title | Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph |
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