Beating critical slowness in symmetry-breaking potentials

A fast method for simulating certain phase transitions has been extended to
a new class of models.

Nature slows way down near continuous phase transitions.  This process, known
as critical slowing down, is characterized by large fluctuations that persist
far longer than the microscopic motion of their constituents suggest.
Computers attempting to simulate nature are slower than nature itself, and the
result can render measurement of critical properties computationally
intractable.  For models of nature with certain symmetries, algorithms exist
that eliminate this slowness with clever and unnatural dynamics, transforming
large clusters of microscopic constituents together in a way that resembles
the natural fluctuations. Unfortunately, these methods cannot be directly
applied in the presence of an external potential, like a magnetic field or
lattice interaction, since these break the symmetry these algorithms depend on
to operate.

We've introduced a way of using cluster algorithms on systems in external
potentials despite broken symmetry. By including the external potential as a
dynamic element of the model that can itself be added to clusters and
transformed along with the rest of the system, the original model's symmetries
are restored.  Characteristic states of the modified model are equivalent to
those of the original one provided the accumulated transformations to the
external potential are accounted for and reversed when making measurements.
The extension naturally preserves the efficiency of the original algorithms in
the places where critical slowing down is worst.