Gibbsianizing nonequilibrium dynamics of artificial spin ice and other spin systems

Beyond effective temperature for nonequilibrium spin systems is the concept of an effective potential, an 'as if' potential with no regard for real energies. But if the former is ad hoc, the latter would surely seem more so. We take up the task of tying a flow of effective interaction in coupling space to specified dynamics, and illustrate what can be done with pencil-and-paper approximations as well as Monte-Carlo integration of the flow equations. This Gibbsianization program is applied to a model of a zero-temperature quench from a completely disordered state as well as a model of artificial spin lattice rotational demagnetization in the disorder-dominated regime. Lessons are drawn regarding the most fruitful effective potentials to use in modelling laboratory systems.