Microscopic here implies that quantum mechanics has to be used to provide an accurate description of the system.
As a consequence, the wave function of the system is a complicated object holding a large amount of information, which usually makes exact or analytical calculations impractical or even impossible.
The dimension of the classical many-body system scales linearly with the number of particles
In quantum mechanics, however, the many-body-system is in general in a superposition of combinations of single particle states - all the
Because the required numerical expense grows so quickly, simulating the dynamics of more than three quantum-mechanical particles is already infeasible for many physical systems.
[1] Thus, many-body theoretical physics most often relies on a set of approximations specific to the problem at hand, and ranks among the most computationally intensive fields of science.
In many cases, emergent phenomena may arise which bear little resemblance to the underlying elementary laws.
Many-body problems play a central role in condensed matter physics.