Zero-Temperature Dynamics in the Dilute Curie–Weiss Model
We consider the Ising model on a dense Erdős–Rényi random graph, G ( N , p ) , with p > 0 fixed—equivalently, a disordered Curie–Weiss Ising model with Ber ( p ) couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper...
Gespeichert in:
| Veröffentlicht in: | Journal of statistical physics 2018-08, Vol.172 (4), p.1009-1028 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1028 |
|---|---|
| container_issue | 4 |
| container_start_page | 1009 |
| container_title | Journal of statistical physics |
| container_volume | 172 |
| creator | Gheissari, Reza Newman, Charles M. Stein, Daniel L. |
| description | We consider the Ising model on a dense Erdős–Rényi random graph,
G
(
N
,
p
)
, with
p
>
0
fixed—equivalently, a disordered Curie–Weiss Ising model with
Ber
(
p
)
couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of
G
(
N
,
p
)
with
p
>
0
fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states. |
| doi_str_mv | 10.1007/s10955-018-2087-9 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_22787981</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A547146824</galeid><sourcerecordid>A547146824</sourcerecordid><originalsourceid>FETCH-LOGICAL-c383t-f73e79c774e741fbba6cca325b5b8421fab7adff4a729804ec66aa029c6cb9283</originalsourceid><addsrcrecordid>eNp1kMtOAyEUQInRxFr9AHeTuKYC8wDiqqnPpMZNjYkbwtBLS9MOFZiFO__BP_RLxIyJK8OCQM4hl4PQOSUTSgi_jJTIusaECsyI4FgeoBGtOcOyoeUhGhHCGK44rY_RSYwbQogUsh6hq1cIHi9gt4egUx-guH7v9M6ZWLiuSOt8dts-QTHrg4Ovj88XcDEWj34J21N0ZPU2wtnvPkbPtzeL2T2eP909zKZzbEpRJmx5CVwazivgFbVtqxtjdMnqtm5FxajVLddLayvNmRSkAtM0WhMmTWNayUQ5RhfDuz4mp6JxCcza-K4DkxRjXHAp6B-1D_6th5jUxvehy4MpRjjjTSabTE0GaqW3oFxnfQra5LWE_GnfgXX5flrnVFUjWJUFOggm-BgDWLUPbqfDu6JE_aRXQ3qV06uf9Epmhw1OzGy3gvA3yv_SN_UWhas</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2072762276</pqid></control><display><type>article</type><title>Zero-Temperature Dynamics in the Dilute Curie–Weiss Model</title><source>SpringerLink Journals - AutoHoldings</source><creator>Gheissari, Reza ; Newman, Charles M. ; Stein, Daniel L.</creator><creatorcontrib>Gheissari, Reza ; Newman, Charles M. ; Stein, Daniel L.</creatorcontrib><description>We consider the Ising model on a dense Erdős–Rényi random graph,
G
(
N
,
p
)
, with
p
>
0
fixed—equivalently, a disordered Curie–Weiss Ising model with
Ber
(
p
)
couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of
G
(
N
,
p
)
with
p
>
0
fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states.</description><identifier>ISSN: 0022-4715</identifier><identifier>EISSN: 1572-9613</identifier><identifier>DOI: 10.1007/s10955-018-2087-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; CONFIGURATION ; Couplings ; Curie temperature ; Dilution ; GRAPH THEORY ; GROUND STATES ; ISING MODEL ; LIMITING VALUES ; Mathematical and Computational Physics ; Minima ; PARTITION ; Physical Chemistry ; Physics ; Physics and Astronomy ; PROBABILITY ; Quantum Physics ; RANDOMNESS ; Statistical Physics and Dynamical Systems ; Theoretical</subject><ispartof>Journal of statistical physics, 2018-08, Vol.172 (4), p.1009-1028</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>COPYRIGHT 2018 Springer</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c383t-f73e79c774e741fbba6cca325b5b8421fab7adff4a729804ec66aa029c6cb9283</citedby><cites>FETCH-LOGICAL-c383t-f73e79c774e741fbba6cca325b5b8421fab7adff4a729804ec66aa029c6cb9283</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10955-018-2087-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10955-018-2087-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/22787981$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Gheissari, Reza</creatorcontrib><creatorcontrib>Newman, Charles M.</creatorcontrib><creatorcontrib>Stein, Daniel L.</creatorcontrib><title>Zero-Temperature Dynamics in the Dilute Curie–Weiss Model</title><title>Journal of statistical physics</title><addtitle>J Stat Phys</addtitle><description>We consider the Ising model on a dense Erdős–Rényi random graph,
G
(
N
,
p
)
, with
p
>
0
fixed—equivalently, a disordered Curie–Weiss Ising model with
Ber
(
p
)
couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of
G
(
N
,
p
)
with
p
>
0
fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states.</description><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>CONFIGURATION</subject><subject>Couplings</subject><subject>Curie temperature</subject><subject>Dilution</subject><subject>GRAPH THEORY</subject><subject>GROUND STATES</subject><subject>ISING MODEL</subject><subject>LIMITING VALUES</subject><subject>Mathematical and Computational Physics</subject><subject>Minima</subject><subject>PARTITION</subject><subject>Physical Chemistry</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>PROBABILITY</subject><subject>Quantum Physics</subject><subject>RANDOMNESS</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>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOAyEUQInRxFr9AHeTuKYC8wDiqqnPpMZNjYkbwtBLS9MOFZiFO__BP_RLxIyJK8OCQM4hl4PQOSUTSgi_jJTIusaECsyI4FgeoBGtOcOyoeUhGhHCGK44rY_RSYwbQogUsh6hq1cIHi9gt4egUx-guH7v9M6ZWLiuSOt8dts-QTHrg4Ovj88XcDEWj34J21N0ZPU2wtnvPkbPtzeL2T2eP909zKZzbEpRJmx5CVwazivgFbVtqxtjdMnqtm5FxajVLddLayvNmRSkAtM0WhMmTWNayUQ5RhfDuz4mp6JxCcza-K4DkxRjXHAp6B-1D_6th5jUxvehy4MpRjjjTSabTE0GaqW3oFxnfQra5LWE_GnfgXX5flrnVFUjWJUFOggm-BgDWLUPbqfDu6JE_aRXQ3qV06uf9Epmhw1OzGy3gvA3yv_SN_UWhas</recordid><startdate>20180801</startdate><enddate>20180801</enddate><creator>Gheissari, Reza</creator><creator>Newman, Charles M.</creator><creator>Stein, Daniel L.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20180801</creationdate><title>Zero-Temperature Dynamics in the Dilute Curie–Weiss Model</title><author>Gheissari, Reza ; Newman, Charles M. ; Stein, Daniel L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c383t-f73e79c774e741fbba6cca325b5b8421fab7adff4a729804ec66aa029c6cb9283</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>CONFIGURATION</topic><topic>Couplings</topic><topic>Curie temperature</topic><topic>Dilution</topic><topic>GRAPH THEORY</topic><topic>GROUND STATES</topic><topic>ISING MODEL</topic><topic>LIMITING VALUES</topic><topic>Mathematical and Computational Physics</topic><topic>Minima</topic><topic>PARTITION</topic><topic>Physical Chemistry</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>PROBABILITY</topic><topic>Quantum Physics</topic><topic>RANDOMNESS</topic><topic>Statistical Physics and Dynamical Systems</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gheissari, Reza</creatorcontrib><creatorcontrib>Newman, Charles M.</creatorcontrib><creatorcontrib>Stein, Daniel L.</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Journal of statistical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gheissari, Reza</au><au>Newman, Charles M.</au><au>Stein, Daniel L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Zero-Temperature Dynamics in the Dilute Curie–Weiss Model</atitle><jtitle>Journal of statistical physics</jtitle><stitle>J Stat Phys</stitle><date>2018-08-01</date><risdate>2018</risdate><volume>172</volume><issue>4</issue><spage>1009</spage><epage>1028</epage><pages>1009-1028</pages><issn>0022-4715</issn><eissn>1572-9613</eissn><abstract>We consider the Ising model on a dense Erdős–Rényi random graph,
G
(
N
,
p
)
, with
p
>
0
fixed—equivalently, a disordered Curie–Weiss Ising model with
Ber
(
p
)
couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of
G
(
N
,
p
)
with
p
>
0
fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10955-018-2087-9</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-4715 |
| ispartof | Journal of statistical physics, 2018-08, Vol.172 (4), p.1009-1028 |
| issn | 0022-4715 1572-9613 |
| language | eng |
| recordid | cdi_osti_scitechconnect_22787981 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS CONFIGURATION Couplings Curie temperature Dilution GRAPH THEORY GROUND STATES ISING MODEL LIMITING VALUES Mathematical and Computational Physics Minima PARTITION Physical Chemistry Physics Physics and Astronomy PROBABILITY Quantum Physics RANDOMNESS Statistical Physics and Dynamical Systems Theoretical |
| title | Zero-Temperature Dynamics in the Dilute Curie–Weiss Model |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T20%3A49%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Zero-Temperature%20Dynamics%20in%20the%20Dilute%20Curie%E2%80%93Weiss%20Model&rft.jtitle=Journal%20of%20statistical%20physics&rft.au=Gheissari,%20Reza&rft.date=2018-08-01&rft.volume=172&rft.issue=4&rft.spage=1009&rft.epage=1028&rft.pages=1009-1028&rft.issn=0022-4715&rft.eissn=1572-9613&rft_id=info:doi/10.1007/s10955-018-2087-9&rft_dat=%3Cgale_osti_%3EA547146824%3C/gale_osti_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2072762276&rft_id=info:pmid/&rft_galeid=A547146824&rfr_iscdi=true |