Two-dimensional Ising model with competing interactions and its application to clusters and arrays of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi></mml:math>-rings and adiabatic quantum computing

O’Hare, Anthony; Kusmartsev, F. V.; Кugel, K. I.; Laad, M. S.

doi:10.1103/physrevb.76.064528

Cited by 12 publications

(6 citation statements)

References 38 publications

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“…There are two ordered (1 and 2) states arising at intermediate temperatures: the conventional antiferromagnetic order at J / J′ > 4, and the double stripes at J / J′ < 4. At low temperatures, such state is a glass, which is similar to the Ising glass described in refs and . For graphene parameters, where ( J / J′ = 3 3/2 ≈ 5.2) the temperature evolution of the buckling structures (“snapshots”) for 100 × 100 lattices is illustrated in Figure .…”

Section: Model For the Transverse Lattice Distortionssupporting

confidence: 59%

“…Their origin is related to a proliferation of the topological defects, such as domain walls, into the ordered stripy states. The situation is reminiscent of the proliferation of topological defects in the Ising model with competing interaction on the square lattice described in refs and . This transformation of the disordered state into ordered one arises already at the temperature T / J′ ≃ 0.1.…”

Section: Model For the Transverse Lattice Distortionsmentioning

confidence: 92%

“…The two competing interactions on a square lattice lead to intrinsic frustrations and rich and unusual phase diagram. , Because of frustrations, the disordered glassy state arises from the ordered one even with decreasing temperature. Here, we show that similar effects are also relevant to graphene.…”

Section: Model For the Transverse Lattice Distortionsmentioning

confidence: 99%

“…Using the methods described in refs and , we have performed intense the transfer matrix and Monte Carlo simulations of the Ising model focusing on the graphene parameters ( J / J′ = 3 3/2 ≈ 5.2). For different 2D crystals, like silicene, forming monolayers on different substrates, the J / J′ ratio can vary within a rather broad range.…”

Section: Model For the Transverse Lattice Distortionsmentioning

confidence: 99%

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A Stable “Flat″ Form of Two-Dimensional Crystals: Could Graphene, Silicene, Germanene Be Minigap Semiconductors?

2012

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The discovery of a flat two-dimensional crystal known as graphene has contradicted Landau-Peierls-Mermin-Wagner arguments that there is no stable flat form of such crystals. Here, we show that the "flat" shape of graphene arises due to a microscopic buckling at the smallest possible interatomic scale. We show that the graphene, silicene, and other two-dimensional crystals are stable due to transverse short-range displacements of appropriate atoms. The distortions are small and form various patterns, which we describe in a framework of Ising model with competing interactions. We show that when temperature decreases, two transitions, disorder into order and order into disorder, arise. The ordered state has a form of stripes where carbon atoms are shifted regularly with respect to the plane. The flat graphene, silicene, or germanene planes look like a microscopic "washboard" with the wavelength of about couple of interatomic spacing of appropriate sublattices, which for graphene is about 1.8-3.6 Å. At lower temperatures, the ordered state transforms into a glass. Because of up-down asymmetry in buckled graphene, silicene and other two-dimensional crystals deposited on substrate, a minibandgap may arise. We derive a criterion for the minigap formation and show how it is related to the buckling and to the graphene-substrate interaction. Because of the bandgap, there may arise new phenomena and in particular a rectification of ac current induced by microwave or infrared radiation. We show that the amplitude of direct current arising at wave mixing of two harmonics of microwave electromagnetic radiation is huge. Moreover, we predict the existence of miniexcitons and a new type of fermionic minipolaritons whose behavior can be controlled by the microwave and terahertz radiation.

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Section: Model For the Transverse Lattice Distortionssupporting

confidence: 59%

Section: Model For the Transverse Lattice Distortionsmentioning

confidence: 92%

Section: Model For the Transverse Lattice Distortionsmentioning

confidence: 99%

Section: Model For the Transverse Lattice Distortionsmentioning

confidence: 99%

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A Stable “Flat″ Form of Two-Dimensional Crystals: Could Graphene, Silicene, Germanene Be Minigap Semiconductors?

2012

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“…On the other hand, this spin system gives rise to a small but clearly observable magnetic hysteresis effect at 5 K. These results suggest that this contribution originates from another mechanism, such as orbital magnetism, possibly associated with the aromatic repeating units of the conjugated polymer backbone. 58,59 It must be mentioned that chirality or the helicity of the stacked polymer chains is not required for this contribution, as similar results are obtained in achiral P3ATs, in which the polymer chains stack in a parallel fashion. 26 In contrast, a clear correlation is observed between the number of Bohr magnetons and the strength of the red-shifted absorption band which originates from multiple, strongly interacting polymer chains.…”

Section: ' Materials and Methodsmentioning

confidence: 69%

Influence of the Supramolecular Organization on the Magnetic Properties of Poly(3-alkylthiophene)s in Their Neutral State

et al. 2011

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b S Supporting Information ' INTRODUCTIONFor almost three decades, π-conjugated polymers have been explored extensively. Besides their optical, electrical, and electronic properties, 1 also the magnetic behavior has been investigated, albeit to a lesser extent. In order for an organic compound to exhibit ferromagnetism, unpaired electrons (spins) should be present. Mostly, spins are intrinsic 2À4 to the material or introduced as radicals, carbenes, or by oxidation. 2,3,5 A second requirement is a pathway by which unpaired spins can mutually interact (spin coupling). 6 In this point of view, a conjugated π-system is ideal to act as a (ferro)magnetic linker between different spins. However, the substitution pattern and the connectivity are crucial parameters to have ferromagnetic spin coupling, aligning spins in the same direction of an external magnetic field. 7 Quite some "high-spin" molecules, 8,9 oligomers, 10 and polymers 11À14 have been reported based on this approach, and remarkable advances have been achieved.Besides the "high-spin" molecules, also some typical conjugated polymers were reported, showing magnetic behavior under very specific conditions. Typical examples are poly(aniline)s, 15À18 poly(pyrrole), 19 regioirregular poly(3-alkylthiophene)s, 20À24 and (substituted) poly(acetylene)s. 25 In all these examples, the materials were chemically or electrochemically doped, introducing spins (polarons). In contrast to these results, we have previously reported on the magnetic behavior of neutral (undoped) poly(thiophene)s carrying an alkyl, alkoxy, or alkylthio side chain. 26 A comparison of the ESR and SQUID data reveals the presence of (at least) two spin systems. A first electron spin system gives rise to a paramagnetic behavior. A second spin system (of which the origin is unknown) results in a superparamagnetic behavior at 300 K and (for most polymers) a ferromagnetic behavior at 5 K. The ESR-active system is not responsible for the ferromagnetic behavior at 5 K. This has been concluded from the fact that it exhibits a paramagnetic behavior and that there is a large discrepancy between the number of spins (S = 1/2), determined by ESR, and the number of Bohr magnetons (magnetic moment of an electron) measured by SQUID magnetometry. Concerning the presence of ferromagnetism and the coercivity, it was found that polymers in which strong π-interactions between stacked polymer chains are present show the highest coercivity. Therefore, it can be hypothesized that these π-interactions determine the ferromagnetic behavior (coercivity).In this article, the influence of supramolecular organization and π-stacking of a chiral substituted, head-to-tail coupled poly-(3-alkylthiophene) (HT-P3AT) on its magnetic behavior is investigated ( Figure 1). First, since aggregate formation is influenced by the molar mass of these polymers, samples with different molar masses were prepared by fractionation. Differences in their ABSTRACT: The influence of the supramolecular behavior on the magnetic properties of head-to-tail ...

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Stable forms of two-dimensional crystals and graphene

O’Hare

Kusmartsev

Кugel

2012

Physica B: Condensed Matter

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Two-dimensional Ising model with competing interactions and its application to clusters and arrays ofπ-rings and adiabatic quantum computing

Cited by 12 publications

References 38 publications

A Stable “Flat″ Form of Two-Dimensional Crystals: Could Graphene, Silicene, Germanene Be Minigap Semiconductors?

A Stable “Flat″ Form of Two-Dimensional Crystals: Could Graphene, Silicene, Germanene Be Minigap Semiconductors?

Influence of the Supramolecular Organization on the Magnetic Properties of Poly(3-alkylthiophene)s in Their Neutral State

Stable forms of two-dimensional crystals and graphene

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