Spin-spin correlation function of the 2D XY model with weak site or bond dilution

Abstract

The spin-spin correlation function of the 2D XY model decays as a power law at all temperatures below the Berezinskii-Kosterlitz-Thouless transition point with a temperature dependent exponent $\eta =\eta (T/J)$ ($J$ is the ferromagnetic coupling strength). It is known from computer experiments that in the 2D XY model with site or bond dilution this exponent depends on concentration $p$ of removed sites/bonds as well. Knowing the slope $\partial \eta /\partial p$ at point $p=0$, one can predict the value of the exponent for small dilution concentrations: $\eta (p)\simeq \eta (0)+p(\partial \eta /\partial p){|}_{p=0}$. As it is shown in this paper, the spin-wave Hamiltonian allows to obtain exact results for this slope: $(\partial \eta /\partial p){|}_{p=0}=T/(2J)+O((T/J{)}^2)$ and $T/(\pi J)+O((T/J{)}^2)$ for site and for bond dilution, respectively.

9 pages, 2 figures

References in corpus (4)

• Influence of quenched dilution on the quasi-long-range ordered phase of the 2d XY model
• Kosterlitz-Thouless transition in planar spin models with bond dilution
• The 2D XY model on a finite lattice with structural disorder: quasi-long-range ordering under realistic conditions
• Interplay of topological and structural defects in the 2D XY model

Cited by in corpus (1)

• Long-range Order and Directional Defect Propagation in the Nonreciprocal XY Model with Vision Cone Interactions