A spin model for cholesteric liquid crystals

A spin model for cholestric liquid crystals is presented. The free energy is obtained in the mean field and from that the director correlation functions. It is found that one of the correlation functions diverges as (k₃² + bk_⊥⁴)^?1 where k₃ is the component of the wave-number parallel to the pitch axis, x_⊥ the component perpendicular to the pitch axis and b is a constant. This divergence persists to all orders in the small parameter q₀a where a is a molecular length and q₀ is 2π over the pitch. This divergence implies that the cholesteric state is unstable with respect to fluctuations.