  We present work in progress using the Logarithmic Linear Relaxation (LLR)
density of states algorithm to analyse first-order phase transitions in
pure-gauge SU(N) Yang--Mills theories, focusing on N = 4 and 6. By using the
LLR algorithm we aim to avoid super-critical slowing down at such transitions.
Motivation for this study comes from composite dark matter models, which may
feature a first-order confinement transition in the early Universe that would
produce a background of gravitational waves. Improving our understanding of
these phase transitions will help probe these models using observations from
future gravitational-wave observatories. In addition to the confinement
transition, we also analyze bulk phase transitions of the lattice theories,
which feature much larger latent heat.

High Energy Physics - Lattice