# GPU Acceleration of Swendson-Wang Dynamics

## TL;DR

This paper presents a GPU-accelerated implementation of cluster algorithms like Swendsen-Wang and Wolff for simulating lattice systems near critical points, achieving significant speedups over serial versions.

## Contribution

It introduces a parallel GPU implementation of cluster algorithms, significantly improving computational efficiency for critical system simulations.

## Key findings

- 17-fold speedup for Swendsen-Wang algorithm
- 90-fold speedup for Wolff clustering algorithm
- Enables faster analysis of critical phenomena in lattice systems

## Abstract

When simulating a lattice system near its critical temperature, local algorithms for modeling the system's evolution can introduce very large autocorrelation times into sampled data. This critical slowing down places restrictions on the analysis that can be completed in a timely manner of the behavior of systems around the critical point. Because it is often desirable to study such systems around this point, a new algorithm must be introduced. Therefore, we turn to cluster algorithms, such as the Swendsen-Wang algorithm and the Wolff clustering algorithm. They incorporate global updates which generate new lattice configurations with little correlation to previous states, even near the critical point. We look to accelerate the rate at which these algorithm are capable of running by implementing and benchmarking a parallel implementation of each algorithm designed to run on GPUs under NVIDIA's CUDA framework. A 17 and 90 fold increase in the computational rate was respectively experienced when measured against the equivalent algorithm implemented in serial code.