  The entanglement between noncomplementary blocks of a many-body system, where
a part of the system forms an ignored environment, is a largely untouched
problem without analytic results. We rectify this gap by studying the
logarithmic negativity between two macroscopic sets of spins in an arbitrary
tripartition of a collection of mutually interacting spins described by the
Lipkin-Meshkov-Glick Hamiltonian. This entanglement measure is found to be
finite and universal at the critical point for any tripartition whereas it
diverges for a bipartition. In this limiting case, we show that it behaves as
the entanglement entropy, suggesting a deep relation between the scaling
exponents of these two independently defined quantities which may be valid for
other systems.
