1 Ocak 2006 Dergi makalesi Açık Erişim

Hinczewski, Michael; Berker, A. Nihat

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  <dc:creator>Hinczewski, Michael</dc:creator>
  <dc:creator>Berker, A. Nihat</dc:creator>
  <dc:date>2006-01-01</dc:date>
  <dc:description>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 &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 &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.</dc:description>
  <dc:identifier>https://aperta.ulakbim.gov.trrecord/93713</dc:identifier>
  <dc:identifier>oai:zenodo.org:93713</dc:identifier>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:source>PHYSICAL REVIEW E 73(6)</dc:source>
  <dc:title>Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an Ising model on a scale-free hierarchical-lattice small-world network</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
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