Infinitely Many Commensurate Phases in a Simple Ising Model

Fisher, Michael E.; Selke, W.

doi:10.1103/physrevlett.44.1502

Cited by 588 publications

(299 citation statements)

References 11 publications

Supporting

Mentioning

285

Contrasting

Unclassified

Order By: Relevance

“…The models with n = 1 are BNNNI (biaxial next-nearest-neighbor Ising) models which are relatives of the ANNNI (anisotropic next-nearest-neighbor Ising) models [8,9,10,11,12,13] with specially adjusted coupling constants, the restrictions of which are dictated by the string geometry. It seems that the model with d = 2, n = 1 does not show a phase-transition [8,14].…”

Section: Model In Higher Dimensionsmentioning

confidence: 99%

Geometrical string and spin systems

1994

View full text Add to dashboard Cite

We formulate the geometrical string which has been proposed in the articles [1, 2, 3] on the euclidean lattice. It is possible to find such spin systems with local interaction which reproduce the same surface dynamics. In the three-dimensional case this spin system is a usual Ising ferromagnet with additional diagonal antiferromagnetic interaction and with specially adjusted coupling constants. In the four-dimensional case the spin system coincides with the gauge Ising system [4] with an additional double-plaquette interaction and also with specially tuned coupling constants. We extend this construction to random walks and random hypersurfaces (membrane and p-branes) of high dimensionality. We compare these spin systems with the eight-vertex model and BNNNI models.

show abstract

Section: Model In Higher Dimensionsmentioning

confidence: 99%

Geometrical string and spin systems

1994

View full text Add to dashboard Cite

show abstract

“…Thus, we restrict our model to six non-zero coupling constants Kn, Ln, n = 1, 2, 3. This is a generalization of the so-called anisotropic next-nearest neighbor Ising (ANNNI) model [11], [12]. Our model differs from the standard ANNNI one by two features: the third-neighbor interaction and the 4 positions of the hand instead of two in the Ising model.…”

mentioning

confidence: 99%

Microscopic model for the magnetic subsystem inHoNi2B2C

Kalatsky

Pokrovsky

1998

Phys. Rev. B

View full text Add to dashboard Cite

We demonstrate that the system of localized magnetic moments in HoNi2B2C can be described by the 4-positional clock model. This model, at a proper choice of the coupling constants, yields several metamagnetic phases in magnetic field at zero temperature in full agreement with the experimental phase diagram. The model incorporates couplings between not nearest neighbors in the direction perpendicular to the ferromagnetic planes. The same model leads to a c-modulated magnetic phase near the Curie temperature. The theoretical value of the modulation wave-vector agrees surprisingly well with that observed by the neutron diffraction experiment without new adjustable parameters.In the works by Rathnayaka et al. In this compound easy magnetization axes are identified with crystallographic directions 110 and 110 . The low temperature magnetization data show the existence of 4 metamagnetic phases. The low field phase has been identified by neutron diffraction experiments [3,5] and magnetic measurements [2] with the antiferromagnetic phase, which we denote symbolically ↑↓. The phase boundaries and magnetization in other phases versus magnetic field found in the experiment [2] can be readily explained by assuming that the remaining three phases are as follows: phase 2 -↑↑↓, phase 3 -↑↑→, and the high-field phase 4 -↑. It means that 2 3 of the spins in the phases 2 and 3 are parallel to one of the easy axes whereas the remaining 1 3 is antiparallel and perpendicular, respectively, to the same axis. Note that all metamagnetic phases are stoichiometric in the meaning that the concentrations of spins parallel, antiparallel, or perpendicular to the reference axis are rational numbers. The phase diagram of HoNi2B2C at zero temperature is especially simple if the components of magnetic field Hx, Hy are chosen as variables. The experimental phase diagram of HoNi2B2C is shown in Fig. 1 (in the original work [2] it has been presented in polar coordinates h, θ h ).Siegrist et al.[9] and Huang et al.[6] determined the structure of Lu and Ho 1:2:2:1 compounds as the body-centered tetragonal lattice with the space group I4/mmm. The xray structure analysis and the neutron-scattering experiments performed by Goldman et al. [3,4] and Grigereit et al. [5][6][7]. showed that an incommensurate modulated magnetic structures with the wave-vectors Kc = 0.915c * and Ka = 0.585a * occur in the temperature range 4.7-6 K. At temperatures below 4.7 K they vanish and an antiferromagnetic reflections corresponding to alternating ferromagnetic ab-planes of Ho 3+ localizad moments appear. Though the spacial arrangement of the phases ↑↑↓ and ↑↑→ can not bee directly derived from the magnetization measurements, it is unplausible that the ferromagnetic in-plane interaction changes suddenly by switching on of the magnetic field. Therefore, we believe that our symbols ↑↑↓ and ↑↑→ correspond to the real spatial sequences of in-plane magnetic moments. In this article we present a simple microscopic model for magnetic subsystem in the 1:2:2:1 compound which expl...

show abstract

“…Such a combination of terms may also allow for the study of Lifshitz-type behavior [66], e.g. as found in axial nextnearest-neighbor Ising (ANNNI) models [67][68][69].…”

Section: B B Unique Featuresmentioning

confidence: 99%

Atom-optics approach to studying transport phenomena

Gadway

2015

Phys. Rev. A

View full text Add to dashboard Cite

We present a simple experimental scheme, based on standard atom optics techniques, to design highly versatile model systems for the study of single particle quantum transport phenomena. The scheme is based on a discrete set of free-particle momentum states that are coupled via momentumchanging two-photon Bragg transitions, driven by pairs of interfering laser beams. In the effective lattice models that are accessible, this scheme allows for single-site detection, as well as site-resolved and dynamical control over all system parameters. We discuss two possible implementations, based on state-preserving Bragg transitions and on state-changing Raman transitions, which respectively allow for the study of nearly arbitrary single particle Abelian U(1) and non-Abelian U(2) lattice models. -for the quantum simulation of myriad physical phenomena, especially those related to condensed matter [4,5].For the study of single electron transport phenomena, photonic [6][7][8][9][10][11] and cold atom [12][13][14][15][16][17][18][19][20] simulators have made great progress in the experimental exploration of disordered and topological systems, while offering largely complementary capabilities and challenges. Photonic simulators generally permit control of system parameters and the detection of probability distributions at the microscopic, site-resolved level. However, the use of real materials as the medium for light transport makes these systems susceptible to inherent disorder in sample preparation [21] and to absorption in the material [22], and makes simulations in higher spatial dimensions and timedependent control of system parameters non-trivial. For cold atoms, pristine and dynamically variable potential landscapes can be constructed based on their interaction with laser light. However, a microscopic control over system parameters is difficult to realize in atomic systems. Moreover, finite temperatures and the absence of hardwall system boundaries have limited the observation of topological phenomena.Here, we propose an atom optics-based [23][24][25][26] approach to the study of coherent transport phenomena, which incorporates many of the desired features of atomic and photonic experimental platforms. The scheme we describe is motivated in spirit by magnetic resonance-based * bgadway@illinois.edu techniques for local manipulation via global field addressing [27,28]. In the context of studying transport phenomena, however, we consider an inhomogeneous landscape of site energies, with unique energy differences between neighboring sites, which defines unique tunneling resonances for each site-to-site link. Combined with global field addressing that can drive transitions between neighboring sites, and in particular by simultaneous driving of many such transitions in an amplitude, frequency, and phase-controlled manner, this would allow for local control over the parameters of a discrete lattice model relevant to myriad coherent transport phenomena.Atom optics offers a natural candidate system featuring a quadratic energy lan...

show abstract

Infinitely Many Commensurate Phases in a Simple Ising Model

Cited by 588 publications

References 11 publications

Geometrical string and spin systems

Geometrical string and spin systems

Microscopic model for the magnetic subsystem inHoNi2B2C

Atom-optics approach to studying transport phenomena

Contact Info

Product

Resources

About