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.

Minor revisions and refs. added; published version of the invited paper in a special issue of "Low Temp. Physics"

References in corpus (12)

• Ising models of quantum frustration
• Magnetic light scattering in low-dimensional quantum spin systems
• Charge ordering and opening of spin gap in NaV_2O_5
• The "devil's staircase" type phase transition in NaV2O5 under high pressure
• Charge Order Driven spin-Peierls Transition in NaV2O5
• X-ray anomalous scattering investigations on the charge order in ${\alpha }^{\prime }$-NaV${}_2$O${}_5$
• X-ray Investigation of the Magneto-elastic Instability of alpha'-NaV2O5
• Effective Charge and Spin Hamiltonian for the Quarter-Filled Ladder Compound ${\alpha }^{\prime }$-NaV${}_2$O${}_5$
• Orthorhombic versus monoclinic symmetry of the charge-ordered state of NaV2O5
• Simultaneous Charge Ordering and Spin Dimerization in Quasi-Two-Dimensional Quarter-Filled Ladders
• Frustrated spin model as a hard-sphere liquid
• The Spin-SAF transition in NaV2O5 induced by spin-pseudospin coupling

Cited by in corpus (7)

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• Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley tree
• Constructing Landau framework for topological order: Quantum chains and ladders
• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
• Infinite cascades of phase transitions in the classical Ising chain
• A study of the (m,d,N)=(1,3,2) Lifshitz point and of the three- dimensional XY universality class by high-temperature bivariate series for the XY models with anisotropic competing interactions
• Topological floating phase in a spatially anisotropic frustrated Ising model