Universality of Striped Morphologies

Edlund, Erik; Jacobi, Martin Nilsson

doi:10.1103/physrevlett.105.137203

Cited by 38 publications

(41 citation statements)

References 23 publications

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“…The setting is the following: consider Ising models defined by the formal Hamiltonian [1,[3][4][5][6][7][8][9]11,23,28,29,31,[33][34][35][36]39,42]. In this paper, we choose the exponent p to satisfy the constraint p > 2d.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Periodic Striped Ground States in Ising Models with Competing Interactions

Giuliani

Seiringer

2016

Commun. Math. Phys.

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Abstract:We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J c ( p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J c ( p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Periodic Striped Ground States in Ising Models with Competing Interactions

Giuliani

Seiringer

2016

Commun. Math. Phys.

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“…Once an interaction scheme has been established, lattice models are usually investigated using either canonical [12] or microcanonical [15] MC methods. The finding that such models reproduce successfully the striped morphology is not surprising at all, since it has been recently proved that stripe patterns are a straightforward consequence of competing isotropic pairwise interactions [16]. The validity of such lattice models therefore cannot be concluded solely by the fact that they reproduce the right patterns under certain combinations of the external parameters.…”

Section: Introductionmentioning

confidence: 88%

A kinetic Monte Carlo study for stripe-like magnetic domains in ferrimagnetic thin films

Tyukodi¹,

Chioar²,

Néda³

2013

Open Physics

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Abstract:The topology and dynamics of stripe-like magnetic domains obtained in a ferrimagnetic garnet subjected to a time-dependent external magnetic field is studied experimentally and theoretically. Experiments are performed on a commercially available magnetic bubble apparatus, allowing the observation of the timeevolution of the magnetic domain structure. The system is modeled by a meso-scale Ising-type lattice model. Exchange and dipolar interactions between the spins, and interaction of the spins with the external magnetic field are considered. The model is investigated by kinetic Monte Carlo simulations with timevarying transition rates. In the limit of low temperatures the elaborated model leads to a magnetic domain topology and dynamics that is similar to the ones observed in the experiments. In the highly non-equilibrium limit with a high driving frequency the model reproduces the experimentally recorded hysteresis loops as well. PACS

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“…It was shown that striped patterns and other modulated phases may emerge [6][7][8][9][10][11][12][13]. A similar scenario occurs in the case of competing short-range forces: superconducting films, magnetic systems, chemical reactions (i.e., Turing patterns), and copolymers [14].…”

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confidence: 99%

“…A single power-law potential yields a monotically decreasing spectrum, but two competing ones can break this monotonicity and allow for the emergence of modulated phases [13] as shown in Fig. 1.…”

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confidence: 99%

Non-mean-field effects in systems with long-range forces in competition

Bachelard

Staniscia²

2012

Phys. Rev. E

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We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.

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Universality of Striped Morphologies

Cited by 38 publications

References 23 publications

Periodic Striped Ground States in Ising Models with Competing Interactions

Periodic Striped Ground States in Ising Models with Competing Interactions

A kinetic Monte Carlo study for stripe-like magnetic domains in ferrimagnetic thin films

Non-mean-field effects in systems with long-range forces in competition

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