Can electroweak bubble walls run away?

In extensions of the Standard Model with SU(2) singlet scalar fields, there can be regions of parameter space for which the electroweak phase transition is first order already at the mean-field level of analysis. We show that in this case the phase interface (bubble wall) can become ultra-relativistic, with the relativistic gamma factor gamma = (1-v_{wall}^2)^{-1/2} growing linearly with the wall’s propagation distance. We provide a simple criterion for determining whether the bubble wall “runs away” in this way or if gamma approaches a terminal value.