with a

Homogeneous External Source

We derive the equation of the critical curve and calculate the
renormalized masses of the
-symmetric
model
in the presence of a homogeneous external source. We do this using the
Gaussian-Perturbative approximation on finite lattices and explicitly
taking the continuum limit. No disabling divergences are found in the
final results, and no renormalization is necessary. We show that the
results give a complete description of the critical behavior of the
model and of the phenomenon of spontaneous symmetry breaking, at the
quantum-field-theoretical level.

We show that the renormalized masses depend on the external source, and
point out the consequences of that fact for the design of computer
simulations of the model. We point out a simple but interesting
consequence of the results, regarding the role of the
model in the Standard Model of high-energy particle physics. Using the
experimentally known values of the mass and of the expectation value of
the Higgs field, we determine uniquely the values of the *bare*
dimensionless parameters and of the model, which turn
out to be small numbers, significantly less that one.