Cooling a long-range interacting system faster via applying an external magnetic field

If a mean-field spin ring interact with a cold external thermal reservoir, the system might first evolve to the paramagnetic metastable state along the paramagnetic path, and then fluctuate around the metastable state for a long period due to an energy barrier. The spin system must absorb sufficient energy from the thermal reservoir to achieve a phase transition to the final ferromagnetic equilibrium state. However, if an external magnetic field is applied to the system, the energy barrier becomes smaller, which can reduce the relaxation time of the system significantly. Moreover, if the magnetic intensity is strong enough, the energy barrier vanishes and the system evolves directly to the equilibrium state.