Keywords: Long-range interaction; spin chain; phase transition; negative heat capacity.
Summary:Long-range interaction systems are quite common in nature. In the d-dimensional system, if the long-distance attenuation of the two-body interaction conforms to the V(r)~r^(-d-a) form. In the past, most of the work on long-range interaction systems only ended with model research, and it is difficult to find the actual system corresponding to it. With the development of quantum optics and cold atom technology, it is now possible to exchange photons between two cold atoms. Processes to construct long-range interactions and are expected to be used to test various theories of long-range interaction systems. In this study, a long-range interaction chain model arranged on a light crystal lattice is studied. Because of its simplicity, it is possible to construct under the existing experimental conditions, and at the same time, it can exhibit various novel properties of long-range interaction systems. First, a long-range interacting Bose system with N spins arranged on a one-dimensional optical lattice and placed in a staggered magnetic field is considered. The forth-order term is introduced to the Hamilton of the system innovatively. Based on Hamilton, the relation between the entropy and the energy of the system is obtained by counting the number of microscopic states. Furthermore, various thermodynamic properties, involving temperature, heat capacity, and spontaneous magnetization have been calculated analytically. The relationship between temperature, heat capacity, and energy has been thoroughly studied by adjusting the parameters of the Hamiltonian function. We find that this system is non-ergodic and can exhibit first-order phase transition, second-order phase transition, or both under some specific condition. In addition, the micro-canonical ensemble predicts negative specific heat regions. When the two long-range interaction system which independent of each other and in the same state is in the negative temperature zone, if we let them thermal contact, they will change to two states with completely different thermodynamic parameters, i.e., macroscopic Heat flow. This phenomenon violates the zeroth law of thermodynamics. Finally, the global microcanonical phase diagram has been constructed. These unusual features do not contradict the standard statistical mechanics and thermodynamics but extend the scope of their effectiveness.