Journal of Physical Studies 6(2), 153–163 (2002)
DOI: https://doi.org/10.30970/jps.06.153

ON LATTICE-GAS SPIN MODELS WITH CHIRAL INTERACTIONS

S. Romano¹, V. Zagrebnov²
¹Istituto Nazionale per la Fisica della Materia e Dipartimento di Fisica ‟A. Volta", Universitá di Pavia
via A. Bassi 6, I–27100, Pavia, Italy
²Université de la Méditerranée and Centre de Physique Théorique,
CNRS-Luminy-Case 907,
F–13288 Marseille Cedex 9, France

We study here lattice-gas models consisting of two-component classical spins (unit vectors), associated with a three-dimensional lattice, and interacting via a pair potential containing both the scalar product of the two spins, and a chiral (twisting) term; such models can be given magnetic and cholesteric interpretations. We prove that the saturated-lattice version of the model possesses an ordering transition at finite temperature; next we go on to the diluted version, and prove the existence of a chemical potential threshold, above which the model produces long-range orientational order at sufficiently low temperatures. We also comment on extensions of these rigorous results to three-component spins.

PACS number(s): 05.50.+q, 61.30.-v, 64.70.-p