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Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions
Authors:George A. Baker  L.P. Benofy  Fred Cooper  Dean Preston
Affiliation:Theoretical Division, Los Alamos National Laboratory, New Mexico 87545,USA
Abstract:We analyze the renormalized strong coupling series for lattice g0φ4 field theory which is a double series in x = M4a4/g0a4?dandy = 1/M2a2, where M is the renormalized mass, a the lattice spacing, g0 the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g0 from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y5 and in x up to x3 show that for fixed lattice spacing a, G/M4?d is a monotonic function of g0 ranging from zero at g0 = 0 to a maximum at g0 = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.
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