Simulation of Field Theories in Wavelet Representation

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.