Multi-dimensional Density of States by Multicanonical Monte Carlo

TL;DR

This paper applies multicanonical Monte Carlo to compute the two-dimensional density of states for an Ising model with three-spin interactions on a sparse network, revealing how frustration affects the density shape.

Contribution

It demonstrates the effective use of multicanonical Monte Carlo for calculating multi-dimensional densities in complex frustrated systems, specifically on a sparse network.

Findings

Density of states shape varies with frustration level

Multicanonical Monte Carlo efficiently computes densities in complex systems

Projection of the distribution provides insights into algorithm efficiency

Abstract

Multi-dimensional density of states provides a useful description of complex frustrated systems. Recent advances in Monte Carlo methods enable efficient calculation of the density of states and related quantities, which renew the interest in them. Here we calculate density of states on the plane (energy, magnetization) for an Ising Model with three-spin interactions on a random sparse network, which is a system of current interest both in physics of glassy systems and in the theory of error-correcting codes. Multicanonical Monte Carlo algorithm is successfully applied, and the shape of densities and its dependence on the degree of frustration is revealed. Efficiency of multicanonical Monte Carlo is also discussed with the shape of a projection of the distribution simulated by the algorithm.