In this Lubos says that Higgs VEV is also called vacuum Higgs condensate which the term used by Prof. Englert in this video. Since the Higgs field is bosonic, I wonder whether this terminology has anything to do with Bose-Einstein condensate or condensation (which occurs in a dilute gas of bosons very close to absolute zero). This answer too by Maimon suggested something similar. Can one explain the similarity and connection of BE condensate and the VEV of Higgs?
Does it mean that the electroweak phase transition is related to the BE condensation of the Higgs field?
A similar question was previously asked here.