# A Performance Study of the 2D Ising Model on GPUs

## TL;DR

This paper evaluates the performance of various GPU implementations for simulating the 2D Ising model, demonstrating significant speedups over existing TPU and FPGA solutions using optimized multi-GPU techniques.

## Contribution

It introduces optimized GPU algorithms for the 2D Ising model, including stencil, matrix multiply, and multi-spin coding approaches, showcasing their superior performance.

## Key findings

- GPU implementations outperform TPU results
- Multi-GPU approach surpasses FPGA simulation speed
- Optimized algorithms enable large lattice simulations efficiently

## Abstract

The simulation of the two-dimensional Ising model is used as a benchmark to show the computational capabilities of Graphic Processing Units (GPUs). The rich programming environment now available on GPUs and flexible hardware capabilities allowed us to quickly experiment with several implementation ideas: a simple stencil-based algorithm, recasting the stencil operations into matrix multiplies to take advantage of Tensor Cores available on NVIDIA GPUs, and a highly optimized multi-spin coding approach. Using the managed memory API available in CUDA allows for simple and efficient distribution of these implementations across a multi-GPU NVIDIA DGX-2 server. We show that even a basic GPU implementation can outperform current results published on TPUs and that the optimized multi-GPU implementation can simulate very large lattices faster than custom FPGA solutions.