Phase transitions in the Higgs model
39
V ( A
B
c
Figure 2.1. The finite-temperature effective potential for the Higgs model when e 4 « A.
Curves A,B,C are for T > TI, T = Te and T < To respectively.
m2(T) = m2 (I _ T2)
(2.52)
r.2 •
o
A maximum and a second (local) minimum of V develop at non-zero values of
tile when
m (T)
(2.53)
2 ~ C;2
and this happens when the temperature drops below Tt where
T2 =
TJ
_
-12>..m 2
2
(2.54)
I - 1 + C2TJ/>..m2 - J..(J.. + 3e2) _ 12C2 > To·
The second minimum is at
~,~ veT) _ v [ ~~I + (I -~I:) 112]
(2.55)
where
21ml
(2.56)
v=- ../i