  Many frustrated spin models on three-dimensional (3D) lattices are currently
being investigated, both experimentally and theoretically, and develop new
types of long-range orders in their respective phase diagrams. They present
finite-temperature phase transitions, most likely in the Heisenberg 3D
universality class. However, the combination between the 3D character and
frustration makes them hard to study. We present here several methods derived
from high-temperature series expansions (HTSEs), which give exact coefficients
directly in the thermodynamic limit up to a certain order; for several 3D
lattices, supplementary orders than in previous literature are reported for the
HTSEs. We introduce an interpolation method able to describe thermodynamic
quantities at $T > T_c$, which we use here to reconstruct the magnetic
susceptibility and the specific heat and to extract universal and non-universal
quantities (for example critical exponents, temperature, energy, entropy, and
other parameters related to the phase transition). While the susceptibility
associated with the order parameter is not usually known for more exotic
long-range orders, the specific heat is indicative of a phase transition for
any kind of symmetry breaking. We present examples of applications on
ferromagnetic and antiferromagnetic models on various 3D lattices and benchmark
our results whenever possible.
