Ordering in two-dimensional Ising models with competing interactions

Abstract

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. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular region of interactions, corresponding to the Ising sector's super-antiferromagnetic (SAF) ground state. The spin-SAF transition in the coupled Ising-XY model into a phase with co-existent SAF Ising (pseudospin) long-range order and a spin gap is considered. Along with destruction of the quantum critical point of the Ising sector, the phase digram of the Ising-XY model can also demonstrate a re-entrance of the spin-SAF phase. 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. Applications of the spin-SAF theory for the transition in the quarter-filled ladder compound NaV2O5 are discussed.

(m,d,N)=(1,3,2)Lifshitz point and the three-dimensionalButera1, Pernici2 2008Phys. Rev. B8061View full textAdd to dashboardCite

“…Competing interactions and LP's are present in a variety of magnetic, ferroelectric, polymeric, liquid crystal systems, in microemulsion models etc., which sometimes have not yet been studied in complete detail theoretically 12,13,14,15,16,17,18,19,20,21 or experimentally 22 and continue to be actively explored. It is also worth to mention that within the lattice approach to Euclidean quantum field theory there is a continuing interest into models of the same or analogous structure 23,24 , which are expected to show a faster approach to the continuum limit.…”

On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree

“…Since due to the competitiveness in amplitude and sign of the couplings and to the presence of loops which gives rise to an explicit frustration, a quite rich scenario of phases can take place both in regular 6,2 and hierarchical lattices 5,13,32,33,35 . Since due to the competitiveness in amplitude and sign of the couplings and to the presence of loops which gives rise to an explicit frustration, a quite rich scenario of phases can take place both in regular 6,2 and hierarchical lattices 5,13,32,33,35 .…”

Topological floating phase in a spatially anisotropic frustrated Ising model

“…However, according to the prediction of Ref. 12, the transition from the high-temperature paramagnetic phase to the SFAF state is not direct but rather involves an intermediate floating phase which will be the main topic of the following sections.…”

“…To properly understand the numerical results we must recall that the paramagnetic and the 4 × 4 phases are separated by the intermediate floating phase 12 which, in particular, does not have a conventional local order parameter.…”

“…It turns out that the anisotropic nn and nnn Ising model has a quite rich phase diagram. 12 In particular, it possesses the superferro-antiferromagnetic (SFAF) or 4 × 4 ground state phase with ordering wave vector q 44 = (π/2, π/2).…”