Entropy and specific heat features of a four spin system at its energy level crossings

A previous study showed that the efficiency of a quantum heat engine utilizing the Lipkin-Meshkov-Glick (LMG) spin system can reach the Carnot limit at low temperatures when the external field reaches the energy level cross points of the ground states. These points occur when different energy levels become degenerate. To delve more into the quantum behavior at the crossing points, this work considered the thermodynamic characteristics of an LMG model consisting of four spins.