Using mixed action as a trial to the modified mean field theory

we calculatethe internal energies Ep of Z(2)

U(l)and SU(2) lattice gauge fields in 4-dimensions。Phase diagram of first order phase transition like Van derwaals curve is obtained for Z(2)group

which cannot be obtained witn any other trial actions. A very steepcrossover in the E_p-β curve for 4-D U(1) group shows the signal of 2nd order phasetransition。 The E_p-β curve for 4-D SU(2) group is smoothx shawing only a single

con-fining phase

The results are in good agrement with the Monte Carlo results both in thestrong-coupling region and crossver region。