论文标题

分析在iSing自旋玻璃杯中的浓缩和衰老期间的景观层次结构

Analysis of landscape hierarchy during coarsening and aging in Ising spin glasses

论文作者

Boettcher, Stefan, Rahman, Mahajabin

论文摘要

我们使用记录动力学(RD),这是对无处不在的弛豫现象学称为“衰老”的粗粒描述,作为一种诊断工具,可以找到区分Ising Spin模型和铁磁铁的能量景观的通用特征。根据RD的说法,淬灭后的非平衡系统依赖于随机产生一系列不可逆的记录范围事件(地震或雪崩)的波动,使该系统能够逃脱复杂的,层次的能源景观中越来越高的元稳定状态。一旦这些记录事件允许系统克服此类障碍,该系统就会通过将以下元素稳定状态略微稳定来放松。在此框架内,可以在Ising Ferromagnet的粗糙动力学和自旋玻璃的衰老之间进行明确的区别,而自旋玻璃的衰老通常被放在同一类别中。为此,我们通过改变玻璃态的抗铁磁键(每个)到明确的铁磁行为的情况下,在抗铁磁键上改变了抗磁力磁磁性,从而在自旋玻璃和铁磁体之间插值。记录事件的积累随着时间的时间在玻璃制度中增长,并且在特定混合物中急剧过渡到铁磁状态,这种激活很快就会饱和。我们对爱德华兹·安德森(Edwards-Anderson)模型以及Sherrington-Kirkpatrick(平均场)自旋玻璃显示了这种效果。尽管这种过渡与前者先前观察到的零温平衡过渡一致,但该转变尚未描述为后者。

We use record dynamics (RD), a coarse-grained description of the ubiquitous relaxation phenomenology known as "aging", as a diagnostic tool to find universal features that distinguish between the energy landscapes of Ising spin models and the ferromagnet. According to RD, a non-equilibrium system after a quench relies on fluctuations that randomly generate a sequence of irreversible record-sized events (quakes or avalanches) that allow the system to escape ever-higher barriers of meta-stable states within a complex, hierarchical energy landscape. Once these record events allow the system to overcome such barriers, the system relaxes by tumbling into the following meta-stable state that is marginally more stable. Within this framework, a clear distinction can be drawn between the coarsening dynamics of an Ising ferromagnet and the aging of the spin glass, which are often put in the same category. To that end, we interpolate between the spin glass and ferromagnet by varying the admixture $p$ of ferromagnetic over anti-ferromagnetic bonds from the glassy state (at 50% each) to wherever clear ferromagnetic behavior emerges. The accumulation of record events grows logarithmic with time in the glassy regime, with a sharp transition at a specific admixture into the ferromagnetic regime where such activations saturate quickly. We show this effect both for the Edwards-Anderson model on a cubic lattice as well as the Sherrington-Kirkpatrick (mean-field) spin glass. While this transition coincides with a previously observed zero-temperature equilibrium transition in the former, that transition has not yet been described for the latter.

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