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Article Dans Une Revue Journal of Mathematical Physics Année : 2020

Nematic first order phase transition for liquid crystals in the van der Waals--Kac limit

Résumé

In this paper we revisit and extend some mathematical aspects of Onsager's theory of liquid crystals that have been investigated in recent years by different communities (statistical mechanics, analysis and probability). We introduce a model of anisotropic molecules with three-dimensional orientations interacting via a Kac-type interaction. We prove that, in the limit in which the range of the interaction is sent to infinity after the thermodynamic limit, the free energy tends to the infimum of an effective energy functionalà la Onsager. We then prove that, if the spherical harmonic transform of the angular interaction has a negative minimum, this effective free energy functional displays a first order phase transition as the total density of the system increases.
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Dates et versions

hal-02494972 , version 1 (29-02-2020)

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  • HAL Id : hal-02494972 , version 1

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Clément Erignoux, Alessandro Giuliani. Nematic first order phase transition for liquid crystals in the van der Waals--Kac limit. Journal of Mathematical Physics, 2020, 61 (10). ⟨hal-02494972⟩
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