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| The Hamiltonian Mean Field model is an iconic model for the study of Hamiltonian systems with long-range interactions. We study the Hamiltonian Mean Field model with a heterogeneous distribution of the rotors' 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 momentum and parameters of the rotors. For unimodal parameter distributions, we find an analytical expression for the modified critical coupling strength in terms of statistical properties of the parameter distributions and confirm our results with numerical simulations. We find numerically that these effects disappear for strongly bimodal parameter distributions. |
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