We study the site-diluted double-exchange (DE) model and its effective Ruderman–Kittel–Kasuya–Yosida-like interactions, where localized spins are randomly distributed, with the use of the Self-learning Monte Carlo (SLMC) method. The SLMC method is an accelerating technique for Markov chain Monte Carlo simulation using trainable effective models. We apply the SLMC method to the site-diluted DE model to explore the utility of the SLMC method for random systems. We check the acceptance rates and investigate the properties of the effective models in the strong coupling regime. The effective two-body spin–spin interaction in the site-diluted DE model can describe the original DE model with a high acceptance rate, which depends on temperature and spin concentration. These results support a possibility that the SLMC method could obtain independent configurations in systems with a critical slowing down near a critical temperature or in random systems where a freezing problem occurs in lower temperatures.

中文翻译：

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双重交换模型中有效的Ruderman–Kittel–Kasuya–Yosida类相互作用：自学习蒙特卡洛方法

我们使用自学习蒙特卡洛（SLMC）方法研究了站点稀释的双交换（DE）模型及其有效的Ruderman-Kittel-Kasuya-Yosida样相互作用，其中局部自旋随机分布。SLMC方法是使用可训练的有效模型进行马尔可夫链蒙特卡洛模拟的一种加速技术。我们将SLMC方法应用于现场稀释的DE模型，以探索SLMC方法在随机系统中的实用性。我们检查了接受率，并研究了强耦合机制下有效模型的性质。在现场稀释的DE模型中有效的两体自旋-自旋相互作用可以描述具有较高接受率的原始DE模型，这取决于温度和自旋浓度。