1 Ocak 2006 Dergi makalesi Açık Erişim

Hinczewski, Michael; Berker, A. Nihat

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/93713</identifier>
  <creators>
    <creator>
      <creatorName>Hinczewski, Michael</creatorName>
      <givenName>Michael</givenName>
      <familyName>Hinczewski</familyName>
    </creator>
    <creator>
      <creatorName>Berker, A. Nihat</creatorName>
      <givenName>A. Nihat</givenName>
      <familyName>Berker</familyName>
    </creator>
  </creators>
  <titles>
    <title>Inverted Berezinskii-Kosterlitz-Thouless Singularity And High-Temperature Algebraic Order In An Ising Model On A Scale-Free Hierarchical-Lattice Small-World Network</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2006</publicationYear>
  <dates>
    <date dateType="Issued">2006-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/93713</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1103/PhysRevE.73.066126</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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  <descriptions>
    <description descriptionType="Abstract">We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks-a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length center dot for p=0 and 1. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562 500 renormalized probability bins to represent the distribution. For p &amp;lt; 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from T-c. For p &amp;gt;= 0.494, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching T-c from below, the magnetization and the susceptibility, respectively, exhibit the singularities of exp(-C/root T-c-T) and exp(D/root T-c-T), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.</description>
  </descriptions>
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