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(1) This calculation is valid to all orders in
, but only to lowest order in
(here
represents either gauge or scalar coupling). Perturbation theory breaks down when
, since powers of
can be canceled by factors that become infrared divergent when the mass vanishes at
. Therefore. equation (3.4) should only be regarded as an estimate. However, we can expect the true critical temperature
to be in the range
, where
is given by equation (3.4). See, e.g., Weinberg (1974) for details.