  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.
