Critical points of the Onsager functional on a sphere

I. Fatkullin, V. Slastikov

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


We study Onsager's model of isotropic-nematic phase transitions with orientation parameter on a sphere. We consider two interaction potentials: the antisymmetric (with respect to orientation inversion) dipolar potential and symmetric Maier-Saupe potential. We prove the axial symmetry and derive explicit formulae for all critical points, thus obtaining their complete classification. Finally, we investigate their stability and construct the corresponding bifurcation diagrams.

Original languageEnglish (US)
Pages (from-to)2565-2580
Number of pages16
Issue number6
StatePublished - Nov 1 2005

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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