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

Author

Listed:
  • Malbouisson, A.P.C.
  • Portugal, R.
  • Svaiter, N.F.

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.

Suggested Citation

  • Malbouisson, A.P.C. & Portugal, R. & Svaiter, N.F., 2001. "A note on the non-perturbative zero-dimensional λϕ4 model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 292(1), pages 485-493.
    • Handle: RePEc:eee:phsmap:v:292:y:2001:i:1:p:485-493
    DOI: 10.1016/S0378-4371(00)00587-2
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