Ordering in Two-Dimensional Ising Models with Competing Interactions
نویسندگان
چکیده
We study the 2D Ising Model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases, occurring only at non-equal diagonal couplings, are predicted. In a particular region of interactions, corresponding to the Ising model’s super-antiferromagnetic (SAF) ground state, we also consider a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains. The spin-pseudospin model’s spin-SAF transition into the phase with co-existent the SAF Ising (pseudospin) long-range order and the spin gap, has the properties analogous to the reported earlier by us (cond-mat/0310494) for a simpler coupled model. Along with destruction of the quantum critical point of the transverse Ising model, the phase digram of the spin-pseudospin model can also demonstrate a re-entrance. A detailed study of the latter is presented. The mechanism of the re-entrance, due to interplay of interactions in the coupled model, and the conditions of its appearance are established.
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