From microcanonical ensemble to canonical ensemble: phase transitions of a spin chain with a long-range interaction

A long-range interacting spin chain placed in a staggered magnetic field can exhibit either first order phase transition or second order phase transition depending on the magnetic field intensity. The first order phase transition of this model is known to be accompanied with the temperature jump phenomenon in the microcanonical ensemble, while this anomalous temperature jump phenomenon can not be observed in the canonical ensemble. We obtain the crossover phase transition properties passing from a microcanonical to a canonical ensemble, by placing this previously isolated spin chain model in contact with a two-level system that acts as a thermal reservoir. The magnitude of the temperature jump monotonically decreases with the increase of the size of the thermal reservoir. And the microcanonical phase diagram can gradually turn into the canonical phase diagram by increasing the number of particles of the reservoir. Graphical abstract