2010
DOI: 10.1103/physrevb.82.184409
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Scaling hypothesis for modulated systems

Abstract: We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power α of the inverse distance. With L being a spatial length characterizing the modulated phase, all thermodynamic quantities are predicted to scale like some power of L, L △(α,d) . The scaling dimensions △(α, d) only depend on the dimensionality of the system d and the exponent α. Scaling predic… Show more

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Cited by 28 publications
(51 citation statements)
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References 63 publications
(102 reference statements)
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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%
“…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%
“…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%
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