The two dimensional O(3) sigma model, just as quantum chromodynamics, is an asymptotically free theory with a mass gap. Therefore, it is an interesting and simple toy model to investigate algorithms for Markov Chain Monte Carlo simulations of quantum chromodynamics. In this talk, we discuss the construction of a trivializing map, a field transformation from a given theory to a trivial one, through a suitably chosen gradient flow.
An analytic solution for the generating functional of this trivializing flow has been obtained by
a perturbative expansion in the flow time. Utilizing this solution allows for new approaches
to be considered when proposing updates for a Markov Chain Monte Carlo algorithm.