Scaling Properties of a Parallel Implementation of the Multicanonical Algorithm

TL;DR

This paper presents an efficient parallel implementation of the multicanonical algorithm, demonstrating good scaling for simple systems like the Ising model but limited performance for more complex systems with phase transitions.

Contribution

It introduces a parallelization approach for the multicanonical method and analyzes its scaling behavior on different lattice models.

Findings

Parallel implementation scales well for the Ising model.

Performance is limited for the 8-state Potts model due to phase transition barriers.

Estimate quality remains consistent in parallel runs.

Abstract

The multicanonical method has been proven powerful for statistical investigations of lattice and off-lattice systems throughout the last two decades. We discuss an intuitive but very efficient parallel implementation of this algorithm and analyze its scaling properties for discrete energy systems, namely the Ising model and the 8-state Potts model. The parallelization relies on independent equilibrium simulations in each iteration with identical weights, merging their statistics in order to obtain estimates for the successive weights. With good care, this allows faster investigations of large systems, because it distributes the time-consuming weight-iteration procedure and allows parallel production runs. We show that the parallel implementation scales very well for the simple Ising model, while the performance of the 8-state Potts model, which exhibits a first-order phase transition, is limited due to emerging barriers and the resulting large integrated autocorrelation times. The quality of estimates in parallel production runs remains of the same order at same statistical cost.