发表机构
Trans-Scale Quantum Science Institute, The University of Tokyo; Institute for Physics of Intelligence, The University of Tokyo（跨尺度量子科学研究所，东京大学; 物理智能研究所，东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种通过辅助高斯场实现全变量同步更新的蒙特卡洛方法，满足细致平衡，适用于GPU并行；在平均场自旋玻璃和随机正交模型中，结合DMFT精确分析，发现FDT在动力学转变温度以下被违反，响应-关联呈广义FDT双斜率形式。
AI 中文摘要
标准马尔可夫链蒙特卡洛方法一次更新一个变量以满足细致平衡，这阻碍了其充分利用图形处理单元（GPU）等大规模并行硬件。我们研究了一种适用于具有成对相互作用的系统的蒙特卡洛方法，其中所有变量同时更新，这通过高斯积分恒等式引入的辅助高斯场得以实现。该方法满足细致平衡，因此保证收敛到正则分布。对于平均场自旋玻璃，其动力学可通过动力学平均场理论（DMFT）精确分析。将该方法和DMFT应用于表现出随机一级相变的随机正交模型，我们发现，在动力学转变温度以下，涨落耗散定理（FDT）被明显违反，响应与关联之间的关系呈现广义FDT的双斜率形式，模拟与理论定量一致。
英文摘要
Standard Markov chain Monte Carlo methods update variables one at a time to satisfy detailed balance, which prevents them from fully exploiting massively parallel hardware such as graphics processing units (GPUs). We study a Monte Carlo method for systems with pairwise interactions in which all variables are updated simultaneously, made possible by auxiliary Gaussian fields introduced through the Gaussian integral identity. The method satisfies detailed balance and is therefore guaranteed to converge to the canonical distribution. For mean-field spin glasses, its dynamics can be analyzed exactly by dynamical mean-field theory (DMFT). Applying the method and the DMFT to the random orthogonal model, which exhibits a random first-order transition, we find that the fluctuation-dissipation theorem (FDT) is clearly violated below the dynamical transition temperature, and that the relation between response and correlation takes the two-slope form of a generalized FDT, with simulations and theory in quantitative agreement.
Comments15 pages, 4 figures, 2 tables
