The vortex instability at the Quantum Hall Conditions

It was shown that the ground states obtained by the projection on the states of the lowest Landau level are unstable due to the formation of the isolated vortex decreasing the energy at the partial Ll fillings.This statement is valid due to the different dependence on the sample size of the various terms in the free energy like the free energy of the rotating liquid irrelevant to the details of the microscopical structure and the interaction.