Conditions for a ferromagnetic ground state of Ising and Heisenberg models with an external magnetic field

ABSTRACT

For the isotropic Heisenberg Hamiltonian with ferromagnetic nearest-, antiferromagnetic next-nearest-neighbor interactions, and an external magnetic field: H=J1Σn,NNS⃗ n⋅S⃗ n+δ1+J2Σn,NNNS⃗ n⋅S⃗ n+δ2−hΣnSzn, J1<0, J2>0 necessary and sufficient conditions for a ferromagnetic ground state are obtained for some Bravais lattices with periodic boundaries and arbitrary spin s. For the square and cubic lattices the sufficient conditions possess a nontrivial s dependence. These conditions are compared with the thresholds for the Ising and classical Heisenberg model. Threshold inequalities are generalized to the case h≠0. The zero-temperature magnetization and susceptibility are discussed for the classical and quantum case. For the square lattice with only 4 sites the magnetization as function of h shows a qualitatively different behavior in the quantum case for |J1|J2<1 and |J1|J2>1, respectively. Sufficient, necessary, and threshold conditions are also derived for the nearest-neighbor antiferromagnet and the Heisenberg model with arbitrary coupling constants (J1,…,Jr) in an external field.

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http://journals.aps.org.sci-hub.tw/prb/abstract/10.1103/PhysRevB.24.2570