First-order phase transition in Onsager's model of hard rods in $\mathbb R^3$
We prove a first-order transition for hard rods in $\mathbb R^3$ whose orientations vary continuously over the sphere. For every sufficiently small positive ratio of diameter to length, the grand-canonical pressure has a nondifferentiable point, with a jump in number density at the intermediate Onsager scale. Following the phase-pressure strategy of Lebowitz, Mazel, and Presutti, we connect coexistence in the homogeneous Onsager functional to the microscopic pressure through an exact auxiliary-field representation, exponential decay of correlations in the rod gas at fixed auxiliary field,…
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