  We study the crossover phase transition of the SU(2) Georgi-Glashow model in
three dimensions. In this model, a confining condensate of topological 't
Hooft-Polyakov monopoles exists in the Higgs regime. We use lattice Monte Carlo
simulations to study the monopole gas across a crossover transition, and
demonstrate that gradient flow can be used to renormalize the otherwise
divergent monopole number density. The condensation of the monopoles means that
the theory admits also a massive photon-like excitation. We show that the
renormalized monopole number density is approximately proportional to the
square of the photon mass, in agreement with semiclassical results. Our results
give insight into behaviour of the Higgs regime near crossover, which has
boarder implications for beyond the Standard Model theories containing adjoint
scalar fields.
