Eleventh-order calculation of Ising-limit Green’s functions for scalar quantum field theory in arbitrary space-time dimensionD

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Abstract
This paper extends an earlier high-temperature lattice calculation of the renormalized Green’s function of a D-dimensional Euclidean scalar quantum field theory in the Ising limit. The previous calculation included all graphs through sixth order. Here, we present the results of an eleventh-order calculation. The extrapolation to the continuum limit in the previous calculation was rather clumsy and did not appear to converge when D>2. Here, we present an improved extrapolation which gives uniformly good results for all real values of the dimension between D=0 and D=4. We find that the four-point Green’s function has the value 0.620±0.007 when D=2 and 0.98±0.01 when D=3 and that the six-point Green’s function has the value 0.96±0.03 when D=2 and 1.2±0.2 when D=3.
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