  We study the Hamiltonian Mean Field (HMF) model of coupled Hamiltonian rotors
with a heterogeneous distribution of moments of inertia and coupling strengths.
We show that when the parameters of the rotors are heterogeneous, finite size
fluctuations can greatly modify the coupling strength at which the incoherent
state loses stability by inducing correlations between the momenta and
parameters of the rotors. When the distribution of initial frequencies of the
oscillators is sufficiently narrow, an analytical expression for the
modification in critical coupling strength is obtained that confirms numerical
simulations. We find that heterogeneity in the moments of inertia tends to
stabilize the incoherent state, while heterogeneity in the coupling strengths
tends to destabilize the incoherent state. Numerical simulations show that
these effects disappear for a wide, bimodal frequency distribution.
