# High-performance parallel computing in the classroom using the public goods game as an example

## TL;DR

This paper demonstrates how accessible graphics cards can significantly accelerate Monte Carlo simulations in statistical physics, enabling live classroom demonstrations of complex phenomena like phase transitions in social dilemma models.

## Contribution

It introduces a practical approach to enhance Monte Carlo simulations using GPUs, with a focus on physics education and providing accessible source code for replication.

## Key findings

- Graphics cards can increase Monte Carlo simulation speed by orders of magnitude.
- The public goods game exhibits a second-order phase transition in the directed percolation class.
- GPU acceleration makes complex simulations feasible for classroom demonstrations.

## Abstract

The use of computers in statistical physics is common because the sheer number of equations that describe the behavior of an entire system particle by particle often makes it impossible to solve them exactly. Monte Carlo methods form a particularly important class of numerical methods for solving problems in statistical physics. Although these methods are simple in principle, their proper use requires a good command of statistical mechanics, as well as considerable computational resources. The aim of this paper is to demonstrate how the usage of widely accessible graphics cards on personal computers can elevate the computing power in Monte Carlo simulations by orders of magnitude, thus allowing live classroom demonstration of phenomena that would otherwise be out of reach. As an example, we use the public goods game on a square lattice where two strategies compete for common resources in a social dilemma situation. We show that the second-order phase transition to an absorbing phase in the system belongs to the directed percolation universality class, and we compare the time needed to arrive at this result by means of the main processor and by means of a suitable graphics card. Parallel computing on graphics processing units has been developed actively during the last decade, to the point where today the learning curve for entry is anything but steep for those familiar with programming. The subject is thus ripe for inclusion in graduate and advanced undergraduate curricula, and we hope that this paper will facilitate this process in the realm of physics education. To that end, we provide a documented source code for an easy reproduction of presented results and for further development of Monte Carlo simulations of similar systems.