Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model
We consider the fluctuations of the free energy for the 2-spin spherical Sherrington–Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian distribution when the temperature is above the critical temperature, and to the GOE Tracy–Widom distributi...
Gespeichert in:
| Veröffentlicht in: | Journal of statistical physics 2016-10, Vol.165 (2), p.185-224 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 224 |
|---|---|
| container_issue | 2 |
| container_start_page | 185 |
| container_title | Journal of statistical physics |
| container_volume | 165 |
| creator | Baik, Jinho Lee, Ji Oon |
| description | We consider the fluctuations of the free energy for the 2-spin spherical Sherrington–Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian distribution when the temperature is above the critical temperature, and to the GOE Tracy–Widom distribution when the temperature is below the critical temperature. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved. |
| doi_str_mv | 10.1007/s10955-016-1610-0 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_1880860836</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A470718454</galeid><sourcerecordid>A470718454</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-2c85b3e9c0c7724cdb0b137f470f4ed1176a422b8cdae411116556831f0539293</originalsourceid><addsrcrecordid>eNp1kLFOwzAQQC0EEqXwAWyRmFPunDh2xqpqAVEEUmG2XMdp06ZxsNOhG__AH_IluApILNiDT-d7d6dHyDXCCAH4rUfIGYsBsxgzhBhOyAAZp3GeYXJKBgCUxilHdk4uvN8AQC5yNiAvs3qvu73qKtv4yJZRtzbRzBkTTRvjVoff1KJdG1dpVUeLELiqWXW2-fr4fKzctlVd-NpGT7Yw9SU5K1XtzdXPOyRvs-nr5D6eP989TMbzWCeMdTHVgi0Tk2vQnNNUF0tYYsLLlEOZmgKRZyqldCl0oUyK4WSMZSLBEliS0zwZkpu-b-vs-974Tm7s3jVhpEQhQGQgkixUjfqqlaqNrJrSdk7pcAuzq7RtTFmF_DhM5ShSlgYAe0A7670zpWxdtVPuIBHk0bTsTctgWh5NSwgM7RnfHsUY92eVf6Fv0rCAFQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1880860836</pqid></control><display><type>article</type><title>Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model</title><source>SpringerLink Journals - AutoHoldings</source><creator>Baik, Jinho ; Lee, Ji Oon</creator><creatorcontrib>Baik, Jinho ; Lee, Ji Oon</creatorcontrib><description>We consider the fluctuations of the free energy for the 2-spin spherical Sherrington–Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian distribution when the temperature is above the critical temperature, and to the GOE Tracy–Widom distribution when the temperature is below the critical temperature. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved.</description><identifier>ISSN: 0022-4715</identifier><identifier>EISSN: 1572-9613</identifier><identifier>DOI: 10.1007/s10955-016-1610-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Critical temperature ; Free energy ; Magnetic fields ; Mathematical and Computational Physics ; Normal distribution ; Physical Chemistry ; Physics ; Physics and Astronomy ; Quantum Physics ; Statistical Physics and Dynamical Systems ; Theoretical</subject><ispartof>Journal of statistical physics, 2016-10, Vol.165 (2), p.185-224</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>COPYRIGHT 2016 Springer</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-2c85b3e9c0c7724cdb0b137f470f4ed1176a422b8cdae411116556831f0539293</citedby><cites>FETCH-LOGICAL-c355t-2c85b3e9c0c7724cdb0b137f470f4ed1176a422b8cdae411116556831f0539293</cites><orcidid>0000-0002-0729-5652</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10955-016-1610-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10955-016-1610-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Baik, Jinho</creatorcontrib><creatorcontrib>Lee, Ji Oon</creatorcontrib><title>Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model</title><title>Journal of statistical physics</title><addtitle>J Stat Phys</addtitle><description>We consider the fluctuations of the free energy for the 2-spin spherical Sherrington–Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian distribution when the temperature is above the critical temperature, and to the GOE Tracy–Widom distribution when the temperature is below the critical temperature. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved.</description><subject>Critical temperature</subject><subject>Free energy</subject><subject>Magnetic fields</subject><subject>Mathematical and Computational Physics</subject><subject>Normal distribution</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>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOwzAQQC0EEqXwAWyRmFPunDh2xqpqAVEEUmG2XMdp06ZxsNOhG__AH_IluApILNiDT-d7d6dHyDXCCAH4rUfIGYsBsxgzhBhOyAAZp3GeYXJKBgCUxilHdk4uvN8AQC5yNiAvs3qvu73qKtv4yJZRtzbRzBkTTRvjVoff1KJdG1dpVUeLELiqWXW2-fr4fKzctlVd-NpGT7Yw9SU5K1XtzdXPOyRvs-nr5D6eP989TMbzWCeMdTHVgi0Tk2vQnNNUF0tYYsLLlEOZmgKRZyqldCl0oUyK4WSMZSLBEliS0zwZkpu-b-vs-974Tm7s3jVhpEQhQGQgkixUjfqqlaqNrJrSdk7pcAuzq7RtTFmF_DhM5ShSlgYAe0A7670zpWxdtVPuIBHk0bTsTctgWh5NSwgM7RnfHsUY92eVf6Fv0rCAFQ</recordid><startdate>20161001</startdate><enddate>20161001</enddate><creator>Baik, Jinho</creator><creator>Lee, Ji Oon</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-0729-5652</orcidid></search><sort><creationdate>20161001</creationdate><title>Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model</title><author>Baik, Jinho ; Lee, Ji Oon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-2c85b3e9c0c7724cdb0b137f470f4ed1176a422b8cdae411116556831f0539293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Critical temperature</topic><topic>Free energy</topic><topic>Magnetic fields</topic><topic>Mathematical and Computational Physics</topic><topic>Normal distribution</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>Baik, Jinho</creatorcontrib><creatorcontrib>Lee, Ji Oon</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of statistical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Baik, Jinho</au><au>Lee, Ji Oon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model</atitle><jtitle>Journal of statistical physics</jtitle><stitle>J Stat Phys</stitle><date>2016-10-01</date><risdate>2016</risdate><volume>165</volume><issue>2</issue><spage>185</spage><epage>224</epage><pages>185-224</pages><issn>0022-4715</issn><eissn>1572-9613</eissn><abstract>We consider the fluctuations of the free energy for the 2-spin spherical Sherrington–Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian distribution when the temperature is above the critical temperature, and to the GOE Tracy–Widom distribution when the temperature is below the critical temperature. The orders of the fluctuations are markedly different in these two regimes. A universality of the limit law is also proved.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10955-016-1610-0</doi><tpages>40</tpages><orcidid>https://orcid.org/0000-0002-0729-5652</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-4715 |
| ispartof | Journal of statistical physics, 2016-10, Vol.165 (2), p.185-224 |
| issn | 0022-4715 1572-9613 |
| language | eng |
| recordid | cdi_proquest_journals_1880860836 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Critical temperature Free energy Magnetic fields Mathematical and Computational Physics Normal distribution Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| title | Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T17%3A23%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Fluctuations%20of%20the%20Free%20Energy%20of%20the%20Spherical%20Sherrington%E2%80%93Kirkpatrick%20Model&rft.jtitle=Journal%20of%20statistical%20physics&rft.au=Baik,%20Jinho&rft.date=2016-10-01&rft.volume=165&rft.issue=2&rft.spage=185&rft.epage=224&rft.pages=185-224&rft.issn=0022-4715&rft.eissn=1572-9613&rft_id=info:doi/10.1007/s10955-016-1610-0&rft_dat=%3Cgale_proqu%3EA470718454%3C/gale_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1880860836&rft_id=info:pmid/&rft_galeid=A470718454&rfr_iscdi=true |