Folds

Dekking, Michel; Poorten, Alf van der

doi:10.1007/bf03023555

Cited by 52 publications

(29 citation statements)

References 6 publications

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“…The three-folding sequence [45] is generated through the substitutions S(0) = 010, S(1) = 011. Starting with 0, after four steps one obtains: The sequence repeats itself if one keeps every third (underlined) term, which gives:…”

Section: Discussionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

“…Two other sequences will be considered in the following: the PF sequence [44] generated through substitutions on pairs of digits, which is studied in appendix A, and the TF sequence [45] studied in Appendix B.…”

Section: Introductionmentioning

confidence: 99%

Marginal Anisotropy in Layered Aperiodic Ising Systems

Berche¹,

Berche²,

Turban³

1996

J. Phys. I France

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“…In 4. FINITE STATE AUTOMATA This short section embeds the material of Sections 1 and 2 into the theory of rational languages [6,7] and automatic sequences [1,3,5]. DEFINITION 4.1.…”

Section: Slmentioning

confidence: 99%

“…= {01, 10, 11} C 3 = {000, 001, 011, 100, 110} C 4 = {0000, 0010, 0100, 0101, 0111, 1001, 1010, 1011, 1101, 1110, 1111} C 5 = {00001, 00010, 00011, 00101, 00110, 00111, 01000, 01010, 01100, 01101, 01111, 10000, 10001, 10011, 10100, 10110, 11000, 11001, 11011, 11100, 11110} The following result describes the cardinalities of the sets …”

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confidence: 99%

An Equivalence Relation on {0,1}*

Bacher

2000

European Journal of Combinatorics

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“…The k-automatic sequences are well-known and have been extensively studied since the 70's [2,5,7,14]. The construction of this kind of sequences is based on the representation of the integers in the base k. For a given integer n, one represents this number in base k using the greedy algorithm and obtains a word [n] k over the alphabet {0, .…”

Section: Introductionmentioning

confidence: 99%

Generalization of automatic sequences for numeration systems on a regular language

Rigo

2000

Theoretical Computer Science

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Let L be an infinite regular language on a totally ordered alphabet (Σ, <). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the output alphabet of the automaton. This process generalizes the concept of k-automatic sequence for abstract numeration systems on a regular language (instead of systems in base k). Here, I study the first properties of these sequences and their relations with numeration systems.

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Folds

Cited by 52 publications

References 6 publications

Marginal Anisotropy in Layered Aperiodic Ising Systems

Marginal Anisotropy in Layered Aperiodic Ising Systems

An Equivalence Relation on {0,1}*

Generalization of automatic sequences for numeration systems on a regular language

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