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

We have done a study of the zero-dimensional $\lambda\phi^{4}$ 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 $Re(\lambda) 0$, it coincides precisely with the exact expression.