Massive-scale simulations of 2D Ising and Blume-Capel models on rack-scale multi-GPU systems

We present high-performance implementations of the two-dimensional Ising and Blume-Capel models for large-scale, multi-GPU simulations. Our approach takes full advantage of the NVIDIA GB200 NVL72 system, which features up to 72 GPUs interconnected via high-bandwidth NVLink, enabling direct GPU-to-GPU memory access across multiple nodes. By utilizing Fabric Memory and an optimized Monte Carlo kernel for the Ising model, our implementation supports simulations of systems with linear sizes up to L = 2^23, corresponding to approximately 70 trillion spins. This allows for a peak processing rate of nearly 1.15 x 10^5 lattice updates per nanosecond—setting a new performance benchmark for Ising model simulations. Additionally, we introduce a custom protocol for computing correlation functions, which strikes an optimal balance between computational efficiency and statistical accuracy. This protocol enables large-scale simulations without incurring prohibitive runtime costs. Benchmark results show near-perfect strong and weak scaling up to 64 GPUs, demonstrating the effectiveness of our approach for large-scale statistical physics simulations.

本研究提出了面向大规模多GPU模拟的二维伊辛（Ising）模型与布卢美-卡佩尔（Blume-Capel）模型的高性能实现方案。该方案充分利用NVIDIA GB200 NVL72系统的算力优势，该系统支持最多72块图形处理器（GPU）通过高带宽NVLink互连，可实现多节点间的直接GPU间内存访问。通过借助Fabric内存以及针对伊辛模型优化的蒙特卡洛（Monte Carlo）核函数，本实现可支持线性尺寸最高达L=2²³的系统模拟，对应约70万亿个自旋位点。此举可实现近1.15×10^5次晶格更新每纳秒的峰值处理速率，为伊辛模型模拟树立了全新的性能基准。此外，本研究还提出了一种用于计算关联函数的定制化协议，该协议在计算效率与统计精度之间实现了最优平衡，可在避免过高运行时间开销的前提下支撑大规模物理模拟任务。基准测试结果显示，当扩展至最多64块GPU时，该方案的强缩放与弱缩放性能均接近完美，验证了其在大规模统计物理模拟中的有效性。