Random fieldxymodel in three dimensions

Abstract

We study random-field xy spin model at T = 0 numerically on lattices of up to 1000 × 1000 × 1000 spins with the accent on the weak random field. Our numerical method is physically equivalent to slow cooling in which the system is gradually losing the energy and relaxing to an energy minimum. The system shows glass properties, the resulting spin states depending strongly on the initial conditions. Random initial condition for the spins leads to the vortex glass (VG) state with short-range spin-spin correlations defined by the average distance between vortex lines. Collinear and some other vortex-free initial conditions result in the vortex-free ferromagnetic (F) states that have a lower energy. The energy difference between the F and VG states correlates with vorticity of the VG state. Correlation functions in the F states agree with the Larkin-Imry-Ma theory at short distances. Hysteresis curves for weak random field are dominated by topologically stable spin walls raptured by vortex loops. We find no relaxation paths from the F, VG, or any other states to the hypothetical vortex-free state with zero magnetization.

Калибровочная Теория Стекольного Перехода В Трехмерной XY-модели С Вмороженным Беспорядком

“…Стеклообразование в трехмерной XY-модели было предметом многочисленных исследо-ваний, основанных как на методах квантовой теории поля [5,6,4,7], так и на вычислительных методах, см., например, [14][15][16][17]. В частности, было промоделировано медленное охлаждение трехмерной XY-модели и проде-монстрировано, что система с первоначально случайно распределенными спинами замораживается в состоянии вихревого стекла [18]. Тем не менее, несмотря на значительные усилия, сам процесс стеклования и его связь с топологическими возбуждениями в XY-системах все еще остается малоизученным.…”

Ordered vs. disordered states of the random-field model in three dimensions

“…For the xy model (n = 2) in three dimensions the properties of that state have been studied in Ref. [3]. In this paper we focus on the comparative study of the F-state in a 3d xy model and in a 3d Heisenberg model (n = 3) with the goal to shed more light on the glassy properties of the RF system.…”

“…[42] In three dimensions strong non-equilbrium effects have been reported in Refs. [43,2,3]. Numerical studies of the 2d elastic media with pinning centers (that is similar to 2d xy model) [44] revealed that pinning creates dislocations and thus destroys the Bragg glass.…”

“…[39], it was suggested in Ref. [3] that the high energy cost of vortex loops was preventing the spins in the xy 3d RF model from relaxing to a disordered state from the initially ordered state. At elevated temperatures, however, the numerical evidence of the power-law decay of correlations in a 2d random-field xy model has been recently obtained by Perret et al [45] In the absence of topological defects, the evidence of the logarithmic growth of misalignment with the size of the system has been also found in 2d Monte Carlo studies of a crystal layer on a disordered substrate and for pinned flux lattices.…”

“…Same R f comes from the Greenfunction method. [9] These ideas have been applied to random magnets, [10,11,12,14] disordered antiferromagnets, [15] spin-glasses, [16] arrays of magnetic bubbles, [17] superconductors, [18,5] charge-density waves, [19] liquid crystals, [20] superconductor-insulator transition, [21] and superfluid 3 He-A in aerogels. [22,23] In early 1980s the renormalization group treatments of the problem by Cardy and Ostlund [24] and by Villain and Fernandez [25] questioned the validity of LarkinImry-Ma (LIM) argument for distances R R f .…”