Monte Carlo simulations and field transformation: the scalar case Original Research Article

We describe a new method in lattice field theory to compute observables at various values of the parameters λi in the action S[φ, λi]. First one performs a single simulation of a “reference action” S[φr, λir] with fixed λir. Then the φr configurations are transformed into those of a field φ distributed according to S[φ, λi], apart from a “remainder action” which enters as a weight. In this way we measure the observables at values of λi different from λir. We study the performance of the algorithm in the case of the simplest renormalizable model, namely the φ4 scalar theory on a four-dimensional lattice and compare the method with the “histogram” technique of which it is a generalization.