Abstract

We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links a can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in a radical way. Small a does not prevent the system from a complete ordering, but this occurs in an extremely (logarithmically) slow manner. However, larger values of this parameter destroy complete ordering, due to frustration, and the evolution is comparatively faster (algebraic). Our study shows a precise correspondence between the kind of developing order, ferromagnetic versus frustrated, and the speed of evolution. The aging properties of the system are studied by focusing on the scaling properties of two-time quantities, the autocorrelation and linear response functions. We find that the contribution of an equilibrium and an aging part to these functions occurs differently in the various regions of the phase diagram of the model. When quenching inside the ferromagnetic phase, the two-time quantities are obtained by the addition of these parts. Instead, in the paramagnetic phase, these two contributions enter multiplicatively. Both of the scaling forms are shown with excellent accuracy, and the corresponding scaling functions and exponents have been determined and discussed.

Graphical abstract

中文翻译：

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沮丧的系统中的生长动力学和老化现象

摘要

我们在带有随机耦合的二维Ising模型中以数字方式研究有序动力学，其中反铁磁链接a的比例可以逐渐调整。我们表明，随着这种比例的增加，行为以根本的方式改变。小a不会阻止系统完成完整的订购，但这会以极（对数）缓慢的方式发生。但是，由于挫败感，该参数的较大值破坏了完整的排序，并且演化相对较快（代数）。我们的研究表明，发展顺序的类型，铁磁与受挫之间的精确对应关系以及进化速度。通过关注二次量的标度特性，自相关和线性响应函数来研究系统的老化特性。我们发现，在模型相图的各个区域中，平衡和老化部分对这些功能的贡献发生的方式不同。在铁磁相内部淬火时，通过添加这些部分可获得两次量。代替，在顺磁阶段，这两个贡献相乘。两种缩放形式均以极高的精度显示，并且已经确定并讨论了相应的缩放函数和指数。

图形概要