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Annealed Ising model with competing interactions on a bethe lattice
Author(s) -
Haroni A. A.,
Paraskevaidis C. E.
Publication year - 1996
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221930219
Subject(s) - antiferromagnetism , bethe lattice , condensed matter physics , ising model , ferromagnetism , paramagnetism , physics , lattice (music) , phase diagram , phase (matter) , quantum mechanics , acoustics
Frustration effects which appear in an annealed Ising‐type system with two types of magnetic atoms (a = A, B) on the sites of a Bethe lattice with branching ratio 2 are studied. Competing magnetic interactions between nearest neighbors (J aa 1) and next‐nearest neigbors (J′ aa 1J″ aa 1) in the presence of an external magnetic field are considered. The distribution of the magnetic atoms on the sites of the Bethe lattice‐is determined, aside from the magnetic interactions, by spin‐independent interactions Ū aa 1, Ū′ aa 1U″ aa 1and by the chemical potential applied to the system. An iterative scheme for the renormalized effective nearest‐neighbor (magnetic) couplings and the effective fields is applied. This scheme reduces the study of an N ‐layer Bethe lattice to the study of a cluster consisting of four lattice points. The effective fields along with the effective nearest‐neigbor couplings of the central cluster contain all the information for the thermodynamic state of the system. The phase diagrams of these systems contain, besides the ferromagnetic and the paramagnetic, a) a four‐cycle antiferromagnetic (AF‐2) phase and b) a modulated phase (M) consisting of commensurate and incommensurate regions. In the case of strong coupling between magnetic atoms of different species, the phase diagrams are enriched by the presence of a modulated antiferromagnetic (MAF) region. The information of modulation persists even within the ferromagnetic phase.