Stripe width and nonlocal domain walls in the two-dimensional dipolar frustrated Ising ferromagnet

Vindigni, Alessandro; Saratz, N.; Portmann, Oliver; Pescia, D.; Politi, Paolo

doi:10.1103/physrevb.77.092414

Cited by 34 publications

(56 citation statements)

References 31 publications

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“…• For T /J 0.3, the period of modulation decreases with temperature, in a similar way to what is found for the stripe width in the Mean-Field Approximation (MFA) of a similar but 2d model and in line with experimental results 20 .…”

Section: Temperature and α-Dependence Of Qαmaxsupporting

confidence: 84%

One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures

Cinti¹,

Portmann

Pescia

et al. 2009

Phys. Rev. B

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We consider a one-dimensional lattice of Ising-type variables where the ferromagnetic exchange interaction J between neighboring sites is frustrated by a long-ranged anti-ferromagnetic interaction of strength g between the sites i and j, decaying as | i − j | −α , with α > 1. For α smaller than a certain threshold α0, which is larger than 2 and depends on the ratio J/g, the ground state consists of an ordered sequence of segments with equal length and alternating magnetization. The width of the segments depends on both α and the ratio J/g. Our Monte Carlo study shows that the onsite magnetization vanishes at finite temperatures and finds no indication of any phase transition. Yet, the modulation present in the ground state is recovered at finite temperatures in the two-point correlation function, which oscillates in space with a characteristic spatial period: The latter depends on α and J/g and decreases smoothly from the ground-state value as the temperature is increased. Such an oscillation of the correlation function is exponentially damped over a characteristic spatial scale, the correlation length, which asymptotically diverges roughly as the inverse of the temperature as T = 0 is approached. This suggests that the long-range interaction causes the Ising chain to fall into a universality class consistent with an underlying continuous symmetry. The e ∆/T temperature dependence of the correlation length and the uniform ferromagnetic ground state, characteristic of the g = 0 discrete Ising symmetry, are recovered for α > α0.

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Section: Temperature and α-Dependence Of Qαmaxsupporting

confidence: 84%

One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures

Cinti¹,

Portmann

Pescia

et al. 2009

Phys. Rev. B

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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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“…Our results are in agreement with previous ones. 17,18 The most notable effect of including higher harmonics is the shrinking of the bubble phase in the h − T plane. The triple point, already present in the single-mode approximation, shifts to higher temperature, and the whole region where the bubble phase is the thermodynamically stable one is considerably reduced near the critical temperature.…”

Section: Introductionmentioning

confidence: 99%

Inverse transition in a two-dimensional dipolar frustrated ferromagnet

et al. 2011

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We show that the mean-field phase diagram of the dipolar frustrated ferromagnet in an external field presents an inverse transition in the field-temperature plane. The presence of this type of transition has recently been observed experimentally in ultrathin films of Fe/Cu(001). We study a coarse-grained model Hamiltonian in two dimensions. The model supports stripe and bubble equilibrium phases, as well as the uniform phase. At variance with common expectations, already in a single-mode approximation, the model shows a sequence of uniform-bubbles-stripes-uniform phase transitions upon lowering the temperature at a fixed external field. Going beyond the single-mode approximation leads to the shrinking of the bubbles phase, which is restricted to a small region near the zero-field critical temperature. Monte Carlo simulations results with a Heisenberg model are consistent with the mean-field results.

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Stripe width and nonlocal domain walls in the two-dimensional dipolar frustrated Ising ferromagnet

Cited by 34 publications

References 31 publications

One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures

One-dimensional Ising ferromagnet frustrated by long-range interactions at finite temperatures

Periodic Striped Ground States in Ising Models with Competing Interactions

Inverse transition in a two-dimensional dipolar frustrated ferromagnet

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