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

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 \ge 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: 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 γ/ν=1.97(10).

References in corpus (15)

• Critical Exponents of the N-vector model
• The critical exponents of the superfluid transition in He4
• Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
• N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}
• High precision Monte Carlo study of the 3D XY-universality class
• Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model
• High Precision Measurement of the Thermal Exponent for the Three-Dimensional XY Universality Class
• Monte Carlo Renormalization of the 3-D Ising model: Analyticity and Convergence
• Finite Size Scaling and ``perfect'' actions: the three dimensional Ising model
• Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory
• On the Critical Exponents for the Λ-Transition in Liquid Helium
• Multi-criticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny's transfer-matrix formalism
• Finite-size scaling of the d=5 Ising model embedded in the cylindrical geometry: An influence of the hyperscaling violation
• Eliminated corrections to scaling around a renormalization-group fixed point: Transfer-matrix simulation of an extended d=3 Ising model
• Multicriticality of the (2+1)-dimensional gonihedric model: A realization of the (d,m)=(3,2) Lifshitz point

Cited by in corpus (7)

• Critical behavior of the Higgs- and Goldstone-mass gaps for the two-dimensional S=1 XY model
• Universal scaled Higgs-mass gap for the bilayer Heisenberg model in the ordered phase
• Deconfined criticality for the S=1 spin model on the spatially anisotropic triangular lattice
• Duality-mediated critical amplitude ratios for the $(2+1)$-dimensional $S=1$ $XY$ model
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
• Deconfined-critical behavior of the VBS- and nematic-order parameters for the spatially anisotropic S=1-spin model
• Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase