Effects of Connectivity Disorder on the Potts Model

Wolfhard Janke, Martin Weigel

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The relevance of quenched, uncorrelated disorder coupling to the local energy density, its paradigm being the random-bond model, is judged by the Harris criterion. A generalization of the underlying argument to the case of spatially correlated disorder, exemplified by quasi-crystals, has been given by Luck. We address the question, whether a relevance criterion of this type is applicable to the case of spin models coupled to different kinds of random graphs. The geometrical fluctuation exponent appearing in Luck’s criterion is precisely determined for the cases of two-dimensional Poissonian Voronoï–Delaunay random lattices and planar, “fat” ϕ3 Feynman diagrams. While previous work for the latter graphs is in accord with the determined relevance threshold, a preliminary analysis of the results of a Monte Carlo simulation of the three-states Potts model on Poissonian Voronoï lattices presented here does not meet the expectations from the relevance criterion.
Original languageEnglish
Pages (from-to)4891-4908
JournalActa Physica Polonica B
Volume34
Issue number10
Publication statusPublished - 2003

Fingerprint

disorders
Feynman diagrams
fats
flux density
exponents
thresholds
crystals
simulation

Bibliographical note

Under a Creative Common License, CC-BY-NC 3.0

Cite this

Effects of Connectivity Disorder on the Potts Model. / Janke, Wolfhard; Weigel, Martin.

In: Acta Physica Polonica B, Vol. 34, No. 10, 2003, p. 4891-4908.

Research output: Contribution to journalArticle

Janke, Wolfhard ; Weigel, Martin. / Effects of Connectivity Disorder on the Potts Model. In: Acta Physica Polonica B. 2003 ; Vol. 34, No. 10. pp. 4891-4908.
@article{7f77ade96ba1459c99fc3b47a6b0a77c,
title = "Effects of Connectivity Disorder on the Potts Model",
abstract = "The relevance of quenched, uncorrelated disorder coupling to the local energy density, its paradigm being the random-bond model, is judged by the Harris criterion. A generalization of the underlying argument to the case of spatially correlated disorder, exemplified by quasi-crystals, has been given by Luck. We address the question, whether a relevance criterion of this type is applicable to the case of spin models coupled to different kinds of random graphs. The geometrical fluctuation exponent appearing in Luck’s criterion is precisely determined for the cases of two-dimensional Poissonian Vorono{\"i}–Delaunay random lattices and planar, “fat” ϕ3 Feynman diagrams. While previous work for the latter graphs is in accord with the determined relevance threshold, a preliminary analysis of the results of a Monte Carlo simulation of the three-states Potts model on Poissonian Vorono{\"i} lattices presented here does not meet the expectations from the relevance criterion.",
author = "Wolfhard Janke and Martin Weigel",
note = "Under a Creative Common License, CC-BY-NC 3.0",
year = "2003",
language = "English",
volume = "34",
pages = "4891--4908",
journal = "Acta Physica Polonica B",
issn = "0587-4254",
publisher = "Jagellonian University",
number = "10",

}

TY - JOUR

T1 - Effects of Connectivity Disorder on the Potts Model

AU - Janke, Wolfhard

AU - Weigel, Martin

N1 - Under a Creative Common License, CC-BY-NC 3.0

PY - 2003

Y1 - 2003

N2 - The relevance of quenched, uncorrelated disorder coupling to the local energy density, its paradigm being the random-bond model, is judged by the Harris criterion. A generalization of the underlying argument to the case of spatially correlated disorder, exemplified by quasi-crystals, has been given by Luck. We address the question, whether a relevance criterion of this type is applicable to the case of spin models coupled to different kinds of random graphs. The geometrical fluctuation exponent appearing in Luck’s criterion is precisely determined for the cases of two-dimensional Poissonian Voronoï–Delaunay random lattices and planar, “fat” ϕ3 Feynman diagrams. While previous work for the latter graphs is in accord with the determined relevance threshold, a preliminary analysis of the results of a Monte Carlo simulation of the three-states Potts model on Poissonian Voronoï lattices presented here does not meet the expectations from the relevance criterion.

AB - The relevance of quenched, uncorrelated disorder coupling to the local energy density, its paradigm being the random-bond model, is judged by the Harris criterion. A generalization of the underlying argument to the case of spatially correlated disorder, exemplified by quasi-crystals, has been given by Luck. We address the question, whether a relevance criterion of this type is applicable to the case of spin models coupled to different kinds of random graphs. The geometrical fluctuation exponent appearing in Luck’s criterion is precisely determined for the cases of two-dimensional Poissonian Voronoï–Delaunay random lattices and planar, “fat” ϕ3 Feynman diagrams. While previous work for the latter graphs is in accord with the determined relevance threshold, a preliminary analysis of the results of a Monte Carlo simulation of the three-states Potts model on Poissonian Voronoï lattices presented here does not meet the expectations from the relevance criterion.

M3 - Article

VL - 34

SP - 4891

EP - 4908

JO - Acta Physica Polonica B

JF - Acta Physica Polonica B

SN - 0587-4254

IS - 10

ER -