Modular symmetry and temperature flow of conductivities in quantum Hall systems with varying Zeeman energy

The behaviour of the critical point between quantum Hall plateaux, as the Zeeman energy is varied, is analysed using modular symmetry of the Hall conductivities following from the law of corresponding states. Flow diagrams for the conductivities as a function of temperature, with the magnetic field fixed, are constructed for different Zeeman energies, for samples with particle-hole symmetry.