Transition from the cholesteric storage mode to the nematic phase in critical restricted geometries

It is shown that a cholesteric liquid crystal, between parallel confining plates of spacing $2L$, prepared in the "storage mode" (helix axis parallel to plates) undergoes a transition to the nematic state when $L$ is decreased to a critical value $L_c$. For $0<\mathrm{}\frac{(L-L_c)}{L_c}\ll 1$ the pitch of the cholesteric helix diverges as $\ln (L-L_c)$.