Vacuum stability in the singlet Majoron model

We study the vacuum stability of the singlet Majoron model using full renormalization group improved scalar potential and Monte Carlo techniques. We show that in the perturbative regime of the various free parameters, the vacuum stability requirement together with LEP limits is passed by 18% of the parameter space if the scale of new physics is 10 TeV and 6% if the scale is $10^{14}$ GeV. Moreover, if the baryogenesis condition for scalar couplings is required, no portion of the parameter space survives.