Simulation of Field Theories in Wavelet Representation

TL;DR

This paper demonstrates that representing 2D ^4 field theory in a wavelet basis and optimizing update ranges significantly reduces autocorrelations and computational costs in simulations.

Contribution

It introduces a wavelet-based simulation method for field theories with optimized update ranges, improving efficiency over traditional local Metropolis methods.

Findings

Reduced autocorrelations in wavelet simulations

Significant decrease in computational requirements

Optimization of update ranges enhances performance

Abstract

The field is expanded in a wavelet series and the wavelet coefficients are varied in a simulation of the 2D $\phi^4$ field theory. The drastically reduced autocorrelations result in a substantial decrease of computing requirements, compared to those in local Metropolis simulations. A large part of the improvement is shown to be the result of an additional freedom in the choice of the allowed range of change at the Metropolis update of wavelet components, namely the range can be optimized independently for all wavelet sizes.