There is some relevant material to be found in the book Statistical Field Theory, by Itzykson and Drouffe (Cambridge University Press), in two volumes. Brief mentions are also to be found in the book The Quantum Theory of Fields, by Weinberg (Cambridge University Press), in three volumes.

A non-trivial tadpole means that the vacuum expectation value of the field may not vanish (either due to multiple classical solutions or due to radiative corrections thereof), since the 1--point function doesn't vanish--that's what the tadpole is. In a theory that respects Lorentz invariance only scalar fields can have non-vanishing 1--point functions.

The way to treat this issue may be found in Coleman and Weinberg's 1973 paper (S.~R.~Coleman and E.~J.~Weinberg,``Radiative Corrections as the Origin of Spontaneous Symmetry Breaking,'' Phys.\ Rev.\ D {\bf 7} (1973) 1888.). The vanishing of the 1--point function about the stable vacuum thus fixes the expectation value of the scalar. The fact that, in general, this expectation value can receive large radiative corrections is known as the ``hierarchy problem''.

Thanks a lot for your answers!

I also find this work helpfull

Steven Weinberg

Calculations of Symmetry Breaking

PRD 7 (1973) 2887