Magnetization and universal sub-critical behaviour in two-dimensional XY magnets

Abstract

AbstracL Layered magneu, considered to be experimental realizations of the w XY model, have a magnetization with a characteristic exponent @ = 0 . 2 . We show, using modified renormalization group equations, that this value of fl is a universal signature of finite-sized w XY behaviour. We present simulation data in agreement with both the calculation and the experimental observations.The two-dimensional XY model has long presented an interesting problem to both theoreticians [I] and experimentalists [2-S]. In the thermodynamic limit, at finite temperatures and in zero magnetic field the model cannot sustain long-range order 191, but nevertheless exhibits a Xosterlitz-Thouless-Berezinsldi' phase transition [lo] involving the unbinding of spin vortices at a critical temperature TKT. In the lowtemperature phase of bound vortices the correlation length remains infinite and the magnetization zero, as a result of the excitation of long-wavelength spin waves. The critical exponents q and 6 vary continuously with temperature [ll], but the exponents p, 7 and U are undefined.Layered Heisenberg magnets with planar anisotropy can be treated as quasi-zD XY systems [12]. In these materials the spontaneous magnetization is stabilized by weak 3D coupling J' which determines the asymptotic critical behaviour. However at lower temperature there is a very sharp crossover to a second regime, which we refer to as 'sub-critical'. The magnetization exponents p measured in thi range are listed in table 1. The compounds BaNi,(PO,),, Rb,CrCI, and K,CuF, are the best approximations to the ideal and represent a variety of lattice types, spin values and degrees of planar anisotropy. All have a well defined p = 0.23. The other compounds in the list have p varying between Using modified renormalization group (RG) equations, we show that the magnetization of an arbitrarily large, but finite, ZD XY model approaches power-law behaviour over a restricted temperature range, with an effective exponent p = 0.23.Thii is a universal properly of the ZDXYmodel and can be regarded, when observed in experiment, as a signature of ZD XY behaviour. We present Monte Carlo simulations in agreement with our calculation, and finally discuss the relationship between the calculation, and the experimental results of table 1.Although there is no broken symmetry in the ZD XY model [9] the spin-spin correlation function has power-law decay at low temperature. This slow decay with 0.18 and -z 0.26 [13].

Hamiltonian dynamics and the phase transition of theXYmodel

“…All our results are in perfect agreement with those of Monte-Carlo simulations (see e.g. [20]), some of them are plotted in the Figs. 1 and 2 for comparison.…”

Quantum Monte Carlo study ofS=12weakly anisotropic antiferromagnets on the square lattice

“…This remarkably shows that the predictions of Ref. 61, derived for the classical 2D planar-rotator model, fully apply also to the quantum nearly-isotropic antiferromagnet we considered.…”

Field Dependence of XY-Behavior in Frustrated S = 1/2 Square Lattices

“…In our context of a quasi-2D system T KT reflects an energy scale of the 2D XY-type spin vortex fluctuations occurring above the AFM order. For this situation Bramwell and Holdsworth calculated that T KT should be approximately 85 % of T N [12]. For the b-parameter experimental values reach from 0.9 (NMR, [13]) to 4.1 (ESR, [10]) which is in agreement with theoretical estimations [11,14].…”