具有挫折耦合的相同振子的二维晶格中的有限尺寸缩放和动力学。

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0247843
Róbert Juhász, Géza Ódor
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引用次数: 0

摘要

考虑了具有相同(零)固有频率和随机受挫耦合的Kuramoto型相互作用的二维振子晶格。我们从微摄动同步态的时间演化出发,数值研究了密切相关的XY自旋玻璃模型的弛豫性质,以及稳定不动点处的性质,稳定不动点也可视为亚稳态。根据我们的研究结果,稳定不动点处的阶参数一般随系统规模呈缓慢的、倒数对数收敛到其极限值。研究发现,对于零中心高斯耦合,无限尺寸极限接近于零,而对于具有足够高的正耦合浓度的二元±1分布,无限尺寸极限明显大于零。此外,松弛时间随系统大小呈代数增长。因此,无限系统中的阶参量在t晚时刻与ln t成反比接近其极限值,类似于在全对全耦合模型中的发现[Daido, Chaos 28, 045102(2018)]。与序参数相反,我们发现对应的XY模型的能量在代数上收敛于它的无穷大极限。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Finite-size scaling and dynamics in a two-dimensional lattice of identical oscillators with frustrated couplings.

A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized states, we study numerically the relaxation properties, as well as properties at the stable fixed point which can also be viewed as a metastable state of the closely related XY spin glass model. According to our results, the order parameter at the stable fixed point shows generally a slow, reciprocal logarithmic convergence to its limiting value with the system size. The infinite-size limit is found to be close to zero for zero-centered Gaussian couplings, whereas, for a binary ±1 distribution with a sufficiently high concentration of positive couplings, it is significantly above zero. Besides, the relaxation time is found to grow algebraically with the system size. Thus, the order parameter in an infinite system approaches its limiting value inversely proportionally to ln⁡t at late times t, similarly to that found in the model with all-to-all couplings [Daido, Chaos 28, 045102 (2018)]. As opposed to the order parameter, the energy of the corresponding XY model is found to converge algebraically to its infinite-size limit.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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