Monte Carlo study of scale-covariant field theories

I investigate the continuum limit of Klauder's field-theory models defined on a hypercubic lattice in four dimensions by mapping this problem onto a statistical-mechanical problem of an analog spin system, with partition function Z = ..integral../sub -infinity//sup infinity/ product/sub x/(dS/sub x//Vertical BarS/sub x/Vertical Bar/sup B/)exp(-A summation/sub x/ S/sub x/ /sup 2/-u/sub 0/ summation/sub x/ S/sub x/ /sup 4/+K x summation/sub x,mu/S/sub x/S/sub x+mu/) and A a given function of u/sub 0/ and B determined from an appropriate normalization condition. Monte Carlo methods are used to determine the phase diagrams and qualitative features of transitions in the regime 0 0 we find a line of first-order transitions for small u/sub 0/, while for larger values of u/sub 0/ there is a line of second-order transitions very similar to the Ising-type transitions of the usual (B = 0) theory, and characterized by vanishing of the renormalized coupling g/sub R/. Only in the latter case can the continuum field theory be defined, and it appears to be trivial free field theory for any choice of the parameter B.