  We introduce a method to measure many-body magic in quantum systems based on
a statistical exploration of Pauli strings via Markov chains. We demonstrate
that sampling such Pauli-Markov chains gives ample flexibility in terms of
partitions where to sample from: in particular, it enables to efficiently
extract the magic contained in the correlations between widely-separated
subsystems, which characterizes the nonlocality of magic. Our method can be
implemented in a variety of situations. We describe an efficient sampling
procedure using Tree Tensor Networks, that exploits their hierarchical
structure leading to a modest $O(\log N)$ computational scaling with system
size. To showcase the applicability and efficiency of our method, we
demonstrate the importance of magic in many-body systems via the following
discoveries: (a) for one dimensional systems, we show that long-range magic
displays strong signatures of conformal quantum criticality (Ising, Potts, and
Gaussian), overcoming the limitations of full state magic; (b) in
two-dimensional $\mathbb{Z}_2$ lattice gauge theories, we provide conclusive
evidence that magic is able to identify the confinement-deconfinement
transition, and displays critical scaling behavior even at relatively modest
volumes. Finally, we discuss an experimental implementation of the method,
which only relies on measurements of Pauli observables.
