Partition function (quantum field theory)

In quantum field theory, we have a generating functional, Z[J] of correlation functions and this value, called the partition function is usually expressed by something like the following functional integral:

$\int {\mathcal {D}}\phi e^{i(S[\phi ]+\int d^{d}xJ(x)\phi (x))}$

where S is the action functional. This is very analogous to statistical mechanics. In fact, a Wick rotation emphasizes the similarities.