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We numerically study the interacting quantum Hall Skyrmion system based on the Chern-Simons action. By noticing that the action is invariant under global spin rotations in the spin space with respect to the magnetic field direction, we obtain the low-energy effective action for a many-Skyrmion system. Performing extensive molecular dynamics simulations, we establish the thermodynamic phase diagram for a many-Skyrmion system.

Thermodynamic Phase Diagram of the Quantum Hall Skyrmion System