Percolation in the harmonic crystal and voter model in three dimensions
We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential U=(J2) summation operatorx,y[phi(x)-phi(y)]2, x,y Z3, J>0, and phi(x) R, a sc...
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| Veröffentlicht in: | Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2006-09, Vol.74 (3 Pt 1), p.031120-031120, Article 031120 |
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| container_issue | 3 Pt 1 |
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| container_title | Physical review. E, Statistical, nonlinear, and soft matter physics |
| container_volume | 74 |
| creator | Marinov, Vesselin I Lebowitz, Joel L |
| description | We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential U=(J2) summation operatorx,y[phi(x)-phi(y)]2, x,y Z3, J>0, and phi(x) R, a scalar height variable, and define occupation variables rhoh(x)=1 (0) for phi(x)>h ( |
| doi_str_mv | 10.1103/PhysRevE.74.031120 |
| format | Article |
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In the first case we start with a Gibbs measure for the potential U=(J2) summation operatorx,y[phi(x)-phi(y)]2, x,y Z3, J>0, and phi(x) R, a scalar height variable, and define occupation variables rhoh(x)=1 (0) for phi(x)>h (<h). The probability p of a site being occupied is then a function of h . In the voter model we consider a stationary measure in which each site is either occupied or empty, with probability p . In both cases the truncated pair correlation of the occupation variables, G(x-y) , decays asymptotically as mid |x-y|-1 . Using some Monte Carlo simulation methods and finite-size scaling we find accurate values of pc as well as the critical exponents for these systems. The latter are different from that of independent percolation in d=3 , as expected from the work of Weinrib and Halperin (WH) for the percolation transition of systems with G(r) approximately r-a [Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent nu is very close to the predicted value of 2, supporting the conjecture by WH that nu=2/a is exact.</description><identifier>ISSN: 1539-3755</identifier><identifier>EISSN: 1550-2376</identifier><identifier>DOI: 10.1103/PhysRevE.74.031120</identifier><identifier>PMID: 17025607</identifier><language>eng</language><publisher>United States</publisher><ispartof>Physical review. 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The latter are different from that of independent percolation in d=3 , as expected from the work of Weinrib and Halperin (WH) for the percolation transition of systems with G(r) approximately r-a [Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent nu is very close to the predicted value of 2, supporting the conjecture by WH that nu=2/a is exact.</description><issn>1539-3755</issn><issn>1550-2376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNpFkE1LAzEURYMotlb_gAvJyt3Ul6_JdCmlVqFgEV2HZOaFjsxMajIt9N_bMhVX7z449y4OIfcMpoyBeFpvDukD94upllMQjHG4IGOmFGRc6PzylMUsE1qpEblJ6RtAcFHIazJiGrjKQY_Jco2xDI3t69DRuqP9BunGxjZ0dUnLeEi9bajtKroPPUbahgqbgYuItKpb7NKxmm7JlbdNwrvznZCvl8Xn_DVbvS_f5s-rrBRS9VmB3JbOggavC9AFyz131jucWYXMKSWq0ys4ZwoqznNpXVV4r5UXDmQhJuRx2N3G8LPD1Ju2TiU2je0w7JLJi5kEKeEI8gEsY0gpojfbWLc2HgwDc9Jn_vQZLc2g71h6OK_vXIvVf-XsS_wCGkxt1Q</recordid><startdate>20060901</startdate><enddate>20060901</enddate><creator>Marinov, Vesselin I</creator><creator>Lebowitz, Joel L</creator><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>20060901</creationdate><title>Percolation in the harmonic crystal and voter model in three dimensions</title><author>Marinov, Vesselin I ; Lebowitz, Joel L</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c345t-8e2acba070f7807816f2bafbe9a5e1b553dbafb322150d2264abd8ff75f3b0483</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><toplevel>online_resources</toplevel><creatorcontrib>Marinov, Vesselin I</creatorcontrib><creatorcontrib>Lebowitz, Joel L</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Physical review. 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In particular the correlation length exponent nu is very close to the predicted value of 2, supporting the conjecture by WH that nu=2/a is exact.</abstract><cop>United States</cop><pmid>17025607</pmid><doi>10.1103/PhysRevE.74.031120</doi><tpages>1</tpages><oa>free_for_read</oa></addata></record> |
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| title | Percolation in the harmonic crystal and voter model in three dimensions |
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