Numerical diagonalization analysis of the criticality of the (2+1) -dimensional XY model: Off-diagonal Novotny's method

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Abstract

The criticality of the (2+1) -dimensional XY model is investigated with the numerical diagonalization method. So far, it has been considered that the diagonalization method would not be very suitable for analyzing the criticality in large dimensions (d≥3); in fact, the tractable system size with the diagonalization method is severely restricted. In this paper, we employ Novotny's method, which enables us to treat a variety of system sizes N=6,8,...,20 (N is the number of spins constituting a cluster). For that purpose, we develop an off-diagonal version of Novotny's method to adopt the off-diagonal (quantum-mechanical XY) interaction. Moreover, in order to improve the finite-size-scaling behavior, we tune the coupling-constant parameters to a scale-invariant point. As a result, we estimate the critical indices as ν=0.675 (20) and γν=1.97 (10).

Original languageEnglish
Article number021135
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume78
Issue number2
DOIs
Publication statusPublished - Aug 27 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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