A note on the non-perturbative zero-dimensional λϕ4 model

A.P.C. Malbouisson, R. Portugal and N.F. Svaiter

Physica A: Statistical Mechanics and its Applications, 2001, vol. 292, issue 1, 485-493

Abstract: We exhibit the partition function of the zero-dimensional λϕ4 model as a simple exact expression in terms of the Macdonald function for Re(λ)>0. Then by analytic continuation, we obtain an expression defined in the complex coupling constant plane λ, for |argλ|<π. Consequently, the partition function understood as an analytic continuation is defined for all values of λ, except for a branch cut along the real negative λ-axis. This shows that at least in zero dimension the partition function can be defined for negative coupling constant (where the integral is formally divergent), provided it has a non-vanishing imaginary part. We also evaluate the partition function on perturbative grounds, using the Borel summation technique and we found that in the common domain of validity, for Re(λ)>0, it coincides precisely with the exact expression. Furthermore, a connection between the non-perturbative zero-dimensional solution and the ultralocal λϕ4 model in arbitrary dimension D is presented.

Keywords: Field theory; Zero dimension; Partition function (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:292:y:2001:i:1:p:485-493

DOI: 10.1016/S0378-4371(00)00587-2

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