Surface magnetization of aperiodic ising quantum chains

Turban, L.; Berche, Bertrand

doi:10.1007/bf01308747

Cited by 11 publications

(17 citation statements)

References 18 publications

(34 reference statements)

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“…The persistence probability in (2.7) can be also evaluated analytically using the techniques of Ref. [27](see Appendix A). For small bias there is a linear δ-dependence:…”

Section: Quasiperiodic (Fibonacci) Environmentmentioning

confidence: 99%

Anomalous diffusion in aperiodic environments

Iglói

Turban²,

Rieger

1999

Phys. Rev. E

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We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the transverse-field Ising model with inhomogeneous couplings we obtain many new analytical results for the random walk problem. In the absence of global bias the qualitative behavior of the diffusive motion of the particle and the corresponding persistence probability strongly depend on the fluctuation properties of the environment. In environments with bounded fluctuations the particle shows normal diffusive motion and the diffusion constant is simply related to the persistence probability. On the other hand in a medium with unbounded fluctuations the diffusion is ultra-slow, the displacement of the particle grows on logarithmic time scales. For the borderline situation with marginal fluctuations both the diffusion exponent and the persistence exponent are continuously varying functions of the aperiodicity. Extensions of the results to disordered media and to higher dimensions are also discussed.

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“…The persistence probability in (2.7) can be also evaluated analytically using the techniques of Ref. [27](see Appendix A). For small bias there is a linear δ-dependence:…”

Section: Quasiperiodic (Fibonacci) Environmentmentioning

confidence: 99%

Anomalous diffusion in aperiodic environments

Iglói

Turban²,

Rieger

1999

Phys. Rev. E

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“…In layered systems, generalizing the McCoy-Wu model, [3][4][5][6] aperiodic distributions of the exchange interactions between successive layers in the Ising model have been considered. [7][8][9][10][11][12] In Ref. 13, the Onsager logarithmic singularity of the specific heat was found to be washed out.…”

Section: Introductionmentioning

confidence: 97%

Crossover between aperiodic and homogeneous surface critical behaviors in multilayered two-dimensional Ising models

Berche

Berche²

1997

Phys. Rev. B

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We investigate the surface critical behavior of two-dimensional multilayered aperiodic Ising models in the extreme anisotropic limit. The system under consideration is obtained by piling up two types of layers with respectively p and q spin rows coupled via nearest neighbor interactions λr and λ, where the succession of layers follows an aperiodic sequence generated through substitution rules. Far away from the critical regime, the correlation length ξ ⊥ , measured in lattice spacing units, in the direction perpendicular to the layers is smaller than the first layer width and the system exhibits the usual behavior of an ordinary surface transition. In the other limit, in the neighborhood of the critical point, ξ ⊥ diverges and the fluctuations are sensitive to the non-periodic structure of the system so that the critical behavior is governed by a new fixed point. We determine the critical exponent associated to the surface magnetization at the aperiodic critical point and show that the expected crossover between the two regimes is well described by a scaling function. From numerical calculations, the parallel correlation length ξ is then found to behave with an anisotropy exponent z which depends on the aperiodic modulation and the layer widths.

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“…where y ts is given by (25), y hs = z − x ms = x ms and b = m n . Taking a first derivative of the surface free energy with respect to h s or t s , one recovers the proper scaling behaviour for the surface magnetization or surface energy, respectively.…”

Section: Introductionmentioning

confidence: 99%

Marginal Anisotropy in Layered Aperiodic Ising Systems

Berche¹,

Berche²,

Turban³

1996

J. Phys. I France

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Abstract. -Two-dimensional layered aperiodic Ising systems are studied in the extreme anisotropic limit where they correspond to quantum Ising chains in a transverse field. The modulation of the couplings follows an aperiodic sequence generated through substitution. According to Luck's criterion, such a perturbation becomes marginal when the wandering exponent of the sequence vanishes. Three marginal sequences are considered: the period-doubling, paperfolding and three-folding sequences. They correspond to bulk perturbations for which the critical temperature is shifted. The surface magnetization is obtained exactly for the three sequences. The scaling dimensions of the local magnetization on both surfaces, xms and xms, vary continuously with the modulation factor. The low-energy excitations of the quantum chains are found to scale as L z with the size L of the system. This is the behaviour expected for a strongly anisotropic system, where z is the ratio of the exponents of the correlation lengths in the two directions. The anisotropy exponent z is here simply equal to xms +xms. The anisotropic scaling behaviour is verified numerically for other surface and bulk critical properties as well.Résumé. -Onétudie des systèmes d'Ising apériodiques en couchesà deux dimensions dans la limite anisotrope extrême où ils correspondentà des chaînes quantiques d'Ising en champ transverse. La modulation des interactions est engendrée par une suite apériodique obtenue par substitution. D'après le critère de Luck, une telle perturbation devient marginale lorsque l'exposant de "divagation" associéà la suite s'annule. Trois suites marginales sont examinées : "doublement de période", "pliage de papier" et "pliage ternaire". Elles correspondentà des perturbations de volume entrainant un changement de température critique. Des expressions exactes de l'aimantation de surface sont obtenues pour les trois suites. Les dimensions anormales de l'aimantation locale sur les deux surfaces, xms et xms, varient continûment avec le facteur de modulation. Les excitations de basseénergie des chaînes quantiques varient en L z avec la taille L du système. C'est là le comportement attendu pour un système fortement anisotrope où z est le rapport des exposants associés aux longueurs de corrélation dans les deux directions. L'exposant d'anisotropie z s'exprime simplement comme la somme des exposants magnétiques xms + xms. Le comportement d'échelle anisotrope est vérifié numériquement pour d'autres propriétés critiques de surface et de volume.(

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Surface magnetization of aperiodic ising quantum chains

Cited by 11 publications

References 18 publications

Anomalous diffusion in aperiodic environments

Anomalous diffusion in aperiodic environments

Crossover between aperiodic and homogeneous surface critical behaviors in multilayered two-dimensional Ising models

Marginal Anisotropy in Layered Aperiodic Ising Systems

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