Study of an Ising model with competing long- and short-range interactions

Löw, U.; Emery, V. J.; Fabricius, K.; Kivelson, Steven

doi:10.1103/physrevlett.72.1918

Cited by 308 publications

(254 citation statements)

References 2 publications

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“…Therefore we will use a 1/R decay of the interaction, V ij = V /|R i − R j |, and the strength of the repulsion is parameterized by V . The V ij are included to counter-act the phase separation tendency of the t − J model 52,5,[53][54][55] , and play a key role in our analysis.…”

Section: Sp(2n ) T-j Model In the Large-n Limitmentioning

confidence: 99%

Competing orders and quantum criticality in doped antiferromagnets

2000

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We use a number of large-N limits to explore the competition between ground states of square lattice doped antiferromagnets which break electromagnetic U(1), time-reversal, or square lattice space group symmetries. Among the states we find are d-, (s * + id)-, and (d x 2 −y 2 + idxy)-wave superconductors, Wigner crystals, Wigner crystals of hole pairs, orbital antiferromagnets (or staggered-flux states), and states with spin-Peierls and bond-centered charge stripe order. In the vicinity of secondorder quantum phase transitions between the states, we go beyond the large-N limit by identifying the universal quantum field theories for the critical points, and computing the finite temperature, quantum-critical damping of fermion spectral functions. We identify candidate critical points for the recently observed quantum-critical behavior in photoemission experiments on Bi2Sr2CaCu2O 8+δ by Valla et al. (Science 285, 2110(Science 285, (1999). These involve onset of a charge density wave, or of broken time-reversal symmetry with d x 2 −y 2 + idxy or s * + id pairing, in a d-wave superconductor. It is not required (although it is allowed) that the stable state in the doped cuprates to be anything other than the d-wave superconductor-the other states need only be stable nearby in parameter space. At finite temperatures, fluctuations associated with these nearby states lead to the observed fermion damping in the vicinity of the nodal points in the Brillouin zone. The cases with broken time-reversal symmetry are appealing because the order parameter is not required to satisfy any special commensurability conditions. The observed absence of inelastic damping of quasiparticles with momenta (π, k), (k, π) (with 0 ≤ k ≤ π) also appears very naturally for the case of fluctuations to d x 2 −y 2 + idxy order.

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Section: Sp(2n ) T-j Model In the Large-n Limitmentioning

confidence: 99%

Competing orders and quantum criticality in doped antiferromagnets

2000

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“…15 Checkerboard patterns in the low-T electronic structure of Ca 2−x Na x CuO 2 Cl 2 have been experimentally observed, 29 and also obtained numerically in simulations of a classical spin-1 lattice gas model with shortrange ferromagnetic coupling and long-range antiferromagnetic Coulomb interactions. 18 There have also been numerical studies 16 of the stripe melting transition in systems governed by Ising-1 / 2 models with short ranged ferromagnetic and long ranged antiferromagnetic couplings. The present model differs from all of these in having an XY rather than an Ising, attractive interaction between the spins.…”

Section: A Model Imentioning

confidence: 99%

“…For example, numerous authors have studied Ising models that include a short-range ͑e.g., ferromagnetic͒ interaction plus a longer-ranged ͑e.g., antiferromagnetic͒ interaction. [15][16][17][18][19][20][21][22][23][24] The origin of those interactions vary, depending on the particular system under study. In studies of magnetic films, for instance, the origin of the ferromagnetic term is the exchange interaction between spins, while the antiferromagnetic term has its origin in dipoledipole interactions.…”

Section: Introductionmentioning

confidence: 99%

Superconductivity versus phase separation, stripes, and checkerboard ordering: A two-dimensional Monte Carlo study

Valdez-Balderas¹,

Stroud²

2005

Phys. Rev. B

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Using Monte Carlo techniques, we study a simple model which exhibits a competition between superconductivity and other types of order in two dimensions. The model is a site-diluted XY model, in which the XY spins are mobile, and also experience a repulsive interaction extending to one, two, or many shells of neighbors. Depending on the strength and range of the repulsion and spin concentration, the spins arrange themselves into a remarkable variety of patterns at low temperatures T, including phase separation, checkerboard order, and straight or labyrinthine patterns of stripes, which sometimes show hints of nematic or smectic order. This pattern formation profoundly affects the superfluid density ␥. Phase separation tends to enhance ␥, checkerboard order suppresses it, and stripe formation increases the component of ␥ parallel to the stripes and reduces the perpendicular one. We verify that ␥͑T =0͒ is proportional to the effective conductance of a random conductance network whose conductances equal the couplings of the XY system. Possible connections between the model and real materials, such as single high-T c cuprate layers, are briefly discussed.

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“…This limit can be studied accurately on large clusters and as anticipated from the spin one model, [10] several CDW phases were observed in the ground state as a function of J/V coul after the 1/r interaction makes the phase separated regime unstable. These CDW phases have an increasing number of electrons in each microscopic cluster as J/V coul grows, since J favors the formation of large spin structures to gain antiferromagnetic energy (see Fig.2).…”

mentioning

confidence: 99%

“…Thus, our results confirm the potential importance of charge-densitywave phases in electronic models for the cuprates. [10,9,11] The analysis of the 2D t-J model is more complicated since there is no analog of k ρ , and the linear cluster sizes are smaller than in 1D. Nevertheless, 2D is the dimension of interest for the cuprates, and it deserves to be explored.…”

mentioning

confidence: 99%

Liaison between superconductivity and phase separation

et al. 1995

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Models of strongly correlated electrons that tend to phase separate are studied including a long-range 1/r repulsive interaction. It is observed that charge-density-wave states become stable as the strength of the 1/r term, V coul , is increased. Due to this effect, the domain of stability of the superconducting phases that appear near phase separation at V coul = 0 is not enlarged by a 1/r interaction as naively expected. Nevertheless, superconductivity exists in a wide region of parameter space, even if phase separation is suppressed.Our results have implications for some theories of the cuprates.Typeset using REVT E X 1

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Study of an Ising model with competing long- and short-range interactions

Cited by 308 publications

References 2 publications

Competing orders and quantum criticality in doped antiferromagnets

Competing orders and quantum criticality in doped antiferromagnets

Superconductivity versus phase separation, stripes, and checkerboard ordering: A two-dimensional Monte Carlo study

Liaison between superconductivity and phase separation

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