Numerical simulations of models and theories that describe complex systems such as spin glasses are becoming increasingly important. Beyond fundamental research, these computational methods also find practical applications in fields like combinatorial optimization. However, Monte Carlo simulations, an important subcategory of these methods, are plagued by a major drawback: they are extremely greedy for (pseudo) random numbers. The total fraction of computer time dedicated to random-number generation increases as the hardware grows more sophisticated, and can get prohibitive for special-purpose computing platforms. We propose here a general-purpose microcanonical simulated annealing (MicSA) formalism that dramatically reduces such a burden. The algorithm is fully adapted to a massively parallel computation, as we show in the particularly demanding benchmark of the three-dimensional Ising spin glass. We carry out very stringent numerical tests of the new algorithm by comparing our results, obtained on GPUs, with high-precision standard (i.e., random-number-greedy) simulations performed on the Janus II custom-built supercomputer. In those cases where thermal equilibrium is reachable (i.e., in the paramagnetic phase), both simulations reach compatible values. More significantly, barring short-time corrections, a simple time rescaling suffices to map the MicSA off-equilibrium dynamics onto the results obtained with standard simulations.

翻译：描述复杂系统（如自旋玻璃）的模型与理论的数值模拟正变得日益重要。除了基础研究之外，这些计算方法还在组合优化等领域找到了实际应用。然而，作为这类方法的重要子类，蒙特卡洛模拟存在一个主要缺陷：它们对（伪）随机数的需求极其贪婪。随着硬件性能的提升，用于随机数生成的计算时间占比不断增加，在专用计算平台上甚至可能变得过高。本文提出了一种通用的微正则模拟退火（MicSA）形式，可显著减轻这一负担。我们以极具挑战性的三维伊辛自旋玻璃为基准进行测试，证明了该算法完全适用于超大规模并行计算。通过将我们在GPU上获得的结果与在Janus II定制超级计算机上执行的高精度标准（即贪婪随机数）模拟结果进行对比，我们对新算法进行了极其严格的数值测试。在可达到热平衡的情况下（即顺磁相），两种模拟得到了兼容的结果。更重要的是，忽略短时间修正后，简单的时标变换就足以将MicSA的非平衡动力学映射到标准模拟获得的结果上。