Finite-size-scaling analysis of the XY universality class between two and three dimensions: An application of Novotny's transfer-matrix method

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Abstract

Based on Novotny's transfer-matrix method, we simulated the (stacked) triangular Ising antiferromagnet embedded in the space with the dimensions variable in the range 2≤d≤≤3. Our aim is to investigate the criticality of the XY universality class for 2≤d≤3. For that purpose, we employed an extended version of the finite-size-scaling analysis developed by Novotny, who utilized this scheme to survey the Ising criticality (ferromagnet) for 1≤d≤3. Diagonalizing the transfer matrix for the system sizes N up to N=17, we calculated the d-dependent correlation-length critical exponent ν(d). Our simulation result ν(d) appears to interpolate smoothly the known two limiting cases, namely, the Kosterlitz-Thouless (KT) and d=3 XY universality classes, and the intermediate behavior bears close resemblance to that of the analytical formula via the 1/N-expansion technique. Methodological details including the modifications specific to the present model are reported.

Original languageEnglish
Article number046112
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume71
Issue number4
DOIs
Publication statusPublished - Apr 2005

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ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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