Title: High-performance parallel computing in the classroom using the public goods game as an example,
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.