  Using the Lebwohl-Lasher interaction for reciprocal local alignment, we
present a comprehensive phase diagram for a dry, apolar, active nematic system
using its stochastic dynamics. The nematic-isotropic transition in this system
is first-order and fluctuation-dominated. Our phase diagram identifies three
distinct regions based on activity and orientational noise relative to
alignment strength: a homogeneous isotropic phase, a nematic phase with giant
density fluctuations, and a coexistence region. Using mean-field analysis and
hydrodynamic theory, we demonstrate that reciprocal interactions lead to a
density fluctuation-induced first-order transition and derive a phase boundary
consistent with numerical results. Quenching from the isotropic to nematic
phase reveals coarsening dynamics with nematic ordering preceding particle
clustering and similar scaling behaviors for density and nematic fields,
exhibiting dynamic exponents between 2 and 3.
