Percolation temperature and the ‘‘instability’’ of the effective potential

Abstract

We show that in spontaneously broken \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ theory the percolation temperature coincides with the temperature at which the semiclassical (loop) expansion of the effective potential (free energy) of the system around a uniform field configuration fails. This allows us to extract the percolation temperature directly from the effective potential. The addition of fermions or gauge fields does not alter the result as long as they are weakly coupled to the scalars. The coincidence holds in the high-temperature limit.