2008/08/27 by Yoshihiro Nishiyama
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Condensed matter physics #Coupling constant #Criticality #Diagonal #Geometry #Mathematics #Nuclear physics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Scale invariance #Scaling #Spins #Statistical physics #Theoretical and Computational Physics #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.78.021135
published as Phys. Rev. E 78, (2008) 021135.
arxiv created 2008/08/27 · openalex publication_date 2008/08/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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> or =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 nu=0.675(20) and gamma/nu=1.97(10).