  A well-known difficulty of perturbative approaches to quantum field theory at
finite temperature is the necessity to address theoretical constraints that are
not present in the vacuum theory. In this work, we use lattice simulations of
scalar correlation functions in massive $\phi^{4}$ theory to analyse the extent
to which these constraints affect the perturbative predictions. We find that
the standard perturbative predictions deteriorate even in the absence of
infrared divergences at relatively low temperatures, and that this is directly
connected to the analytic structure of the propagators used in the expansion.
This suggests that the incorporation of non-perturbative thermal effects in the
propagators is essential for a consistent perturbative formulation of scalar
quantum field theories at finite temperature. By utilising the spectral
constraints imposed on finite-temperature correlation functions, we explore how
these effects manifest themselves in the lattice data, and discuss why the
presence of distinct thermoparticle excitations provides a potential resolution
to these issues.
