A Non-perturbative Solution of the Zero-Dimensional lambda phi^4 Field Theory

Abstract

We have done a study of the zero-dimensional $\lambda {\varphi }^4$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda )>0$. Secondly, an analytic continuation of the partition function for $Re(\lambda )<0$ is performed, and we obtain an expression defined in the complex coupling constant plane $\lambda$, for $|arg\lambda |<\pi$. Consequently, the partition function understood as an analytic continuation is defined for all values of $\lambda$, except for a branch cut along the real negative $\lambda$ axis. 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 $Re(\lambda )>0$, it coincides precisely with the exact expression.

11 pages, 2 figures

References in corpus (2)

• Quenched Random Graphs
• Spin Glasses on Thin Graphs

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