Scaling hypothesis for modulated systems

Portmann, Oliver; Gölzer, A.; Saratz, N.; Billoni, Orlando V.; Pescia, D.; Vindigni, Alessandro

doi:10.1103/physrevb.82.184409

Cited by 28 publications

(51 citation statements)

References 63 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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“…First, we have found that, already in the single-mode approximation, the external field-temperature phase diagram shows an inverse symmetry-breaking transition between paramagnetic and modulated phases, as recently predicted based on scaling arguments and confirmed by experiments on ultrathin ferromagnetic films. 4,13,14 The presence, and experimental relevance, of the inverse transitions was not considered previously in the context of the mean-field phase diagram. From a theoretical point of view, although the generic presence of inverse transitions in this kind of systems was proposed as a consequence of scaling in the behavior of the characteristic lengths with temperature, 14 we have found that the h − T phase diagram shows a maximum even when scaling is not expected to occur.…”

Section: Discussionmentioning

confidence: 99%

“…4,13,14 The presence, and experimental relevance, of the inverse transitions was not considered previously in the context of the mean-field phase diagram. From a theoretical point of view, although the generic presence of inverse transitions in this kind of systems was proposed as a consequence of scaling in the behavior of the characteristic lengths with temperature, 14 we have found that the h − T phase diagram shows a maximum even when scaling is not expected to occur. This seems to be a very basic property of systems with competing interactions in external fields.…”

Section: Discussionmentioning

confidence: 99%

“…12 Interestingly, this seemingly established picture of the mean-field phase diagram was recently put in question, both from experimental results on ultrathin films of Fe/Cu(001) 4,13 and also from a theoretical point of view. 14 The experiments on Fe/Cu(001) show convincingly an inverse transition sequence uniform-modulated-uniform when cycling in temperature at a fixed external applied field. In a recent work, Portmann et al 14 addressed the question about the origin of this inverse symmetry-breaking transition in the context of a scaling hypothesis proposed by the authors.…”

Section: Introductionmentioning

confidence: 99%

“…14 The experiments on Fe/Cu(001) show convincingly an inverse transition sequence uniform-modulated-uniform when cycling in temperature at a fixed external applied field. In a recent work, Portmann et al 14 addressed the question about the origin of this inverse symmetry-breaking transition in the context of a scaling hypothesis proposed by the authors. The critical field line h c (T ), which separates the modulated from the uniform phases, is a consequence of the balance between the dipolar energy, which favors the presence of domains, and the external field energy, which favors a uniform state.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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Formation of Stripes and Slabs Near the Ferromagnetic Transition

Giuliani

Lieb

Seiringer

2014

Commun. Math. Phys.

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We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance) −p , p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c , then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → J − c . (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0 (J)/e S (J) tends to 1 as J → J − c , with e S (J) being the energy per site of the optimal periodic striped/slabbed state and e 0 (J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0 (J) − e S (J) at small but finite J c − J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.

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Scaling hypothesis for modulated systems

Cited by 28 publications

References 63 publications

Periodic Striped Ground States in Ising Models with Competing Interactions

Periodic Striped Ground States in Ising Models with Competing Interactions

Inverse transition in a two-dimensional dipolar frustrated ferromagnet

Formation of Stripes and Slabs Near the Ferromagnetic Transition

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