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Physics Letters A

The Bethe lattice with ferromagnetic and antiferromagnetic interactions in an external magnetic field: Two atoms per site

Erhan Albayrak

Published Aug 13, 2025• 2 citations
Publisher
DOI
10.1016/j.physleta.2025.130894

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Two-layer Bethe lattice whose lattice sites are occupied with spin-3/2 atoms is solved exactly by using the recursion relations in a pairwise approach for given coordination numbers q = 3, 4 and 6 with equal external magnetic fields acting on the layers.The ferromagnetic (FM) and antiferromagnetic (AFM) interactions for the spins of the upper and lower layers, respectively, and either FM or AFM type interactions between the adjacent spins of the layers are assumed.The phase diagrams of the model are studied on different planes for given system parameters by obtaining the ground state (GS) phase diagrams and the thermal variations of the order parameters and the response functions, i. e. the susceptibility and the specific heat, in detail.It was found that the model presents both second-and first-order phase transitions.The reentrant behavior is seen when the model presents two N éel temperatures for higher q values.The existence of the tricritical point and critical end points is also confirmed.
The spin -½ Heisenberg antiferromagnet Hamiltonian with exchange integral and applied external magnetic field is studied with the help of direct exact diagonalization technique. Two site cluster lattices with open boundary conditions are considered and the criteria for the occurrence of a transition from antiferromagnetic (AFM) phase to a ferromagnetic (FM) phase are discussed.However, the results obtained shows that the temperature dependence of the uniform magnetization depends on the strength of the applied magnetic field h. If the applied magnetic field is smaller than the critical field strength, the zero temperature magnetization vanishes, otherwise it is activated.
In this article, we investigate thermal entanglements of the two-site, three-site and four-site mixed spin (1/2,1) XYsystems. The entanglement versus temperature and external magnetic field is discussed. It is found that the entanglements decrease monotonically as temperature increases in the presence and absence of a weak external magnetic field. For the two-site and four-site XY systems, thermal entanglements disappear at the same temperature which is called critical temperature no matter in the ferromagnetic case or antiferromagnetic. It also shows that the critical temperature is independent of external magnetic field. For the three-site system, the corresponding critical temperature is also irrelevant to external magnetic field, while the critical temperature for the ferromagnetic case is higher than that for the antiferromagnetic case. The entanglement of XY systems can develop a few stable platform in an environment of low temperature, but the entanglement vanishes when external magnetic field exceeds some critical value. In this article, we also analyze the difference in thermal entanglement between mixed-spin system and single-spin system, and find that there exists multi-level level crossing in the mixed-spin system.