  Many observables in quantum field theories are involved non-analytic
functions of the parameters of the theory. However, it is expected that they
are not arbitrarily wild, but rather have only a finite amount of geometric
complexity. This expectation has been recently formalized by a tameness
principle: physical observables should be definable in o-minimal structures and
their sharp refinements. In this work, we show that a broad class of
non-analytic partition and correlation functions are tame functions in the
o-minimal structure known as $\mathbb{R}_{\mathscr{G}}$ - the structure
defining Gevrey functions. Using a perturbative approach, we expand the
observables in asymptotic series in powers of a small coupling constant.
Although these series are often divergent, they can be Borel-resummed in the
absence of Stokes phenomena to yield the full partition and correlation
functions. We show that this makes them definable in $\mathbb{R}_{\mathscr{G}}$
and provide a number of motivating examples. These include certain
0-dimensional quantum field theories and a set of higher-dimensional quantum
field theories that can be analyzed using constructive field theory. Finally,
we discuss how the eigenvalues of certain Hamiltonians in quantum mechanics are
also definable in $\mathbb{R}_{\mathscr{G}}$.
