Susceptibility calculations in periodic and quasiperiodic planar Ising models

Helen Au-Yang; Jacques H.H. Perk

doi:10.1016/S0378-4371(02)01780-6

Susceptibility calculations in periodic and quasiperiodic planar Ising models

Helen Au-Yang^*, Jacques H.H. Perk

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

9 Citations (Scopus)

Abstract

New results are presented for the wavevector-dependent susceptibility of Z-invariant periodic and quasiperiodic Ising models in the scaling limit, generalizing old results of Tracy and McCoy for the square lattice. Explicit results are worked out for the two leading singular terms of the susceptibility on four regular isotropic lattices. The methods used provide a proof of the extended lattice-lattice scaling hypothesis for the class of models under consideration.

Original language	English
Pages (from-to)	81-89
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	321
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-4371(02)01780-6
Publication status	Published - 1 Apr 2003
Externally published	Yes
Event	Statphys - Taiwan - 2002: Lattice Models and Complex Systems - Taipei and Taichung, Taiwan Duration: 26 May 2002 → 1 Jun 2002

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10.1016/S0378-4371(02)01780-6

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title = "Susceptibility calculations in periodic and quasiperiodic planar Ising models",

abstract = "New results are presented for the wavevector-dependent susceptibility of Z-invariant periodic and quasiperiodic Ising models in the scaling limit, generalizing old results of Tracy and McCoy for the square lattice. Explicit results are worked out for the two leading singular terms of the susceptibility on four regular isotropic lattices. The methods used provide a proof of the extended lattice-lattice scaling hypothesis for the class of models under consideration.",

keywords = "Corrections to scaling, Fibonacci sequences, Ising model, Lattice-lattice scaling, Painlev{\'e} functions, Penrose tilings, Scaling limit, Wavevector-dependent susceptibility, Z-invariance",

author = "Helen Au-Yang and Perk, {Jacques H.H.}",

year = "2003",

month = apr,

day = "1",

doi = "10.1016/S0378-4371(02)01780-6",

language = "English",

volume = "321",

pages = "81--89",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier B.V.",

number = "1-2",

note = "Statphys - Taiwan - 2002: Lattice Models and Complex Systems ; Conference date: 26-05-2002 Through 01-06-2002",

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TY - JOUR

T1 - Susceptibility calculations in periodic and quasiperiodic planar Ising models

AU - Au-Yang, Helen

AU - Perk, Jacques H.H.

PY - 2003/4/1

Y1 - 2003/4/1

N2 - New results are presented for the wavevector-dependent susceptibility of Z-invariant periodic and quasiperiodic Ising models in the scaling limit, generalizing old results of Tracy and McCoy for the square lattice. Explicit results are worked out for the two leading singular terms of the susceptibility on four regular isotropic lattices. The methods used provide a proof of the extended lattice-lattice scaling hypothesis for the class of models under consideration.

AB - New results are presented for the wavevector-dependent susceptibility of Z-invariant periodic and quasiperiodic Ising models in the scaling limit, generalizing old results of Tracy and McCoy for the square lattice. Explicit results are worked out for the two leading singular terms of the susceptibility on four regular isotropic lattices. The methods used provide a proof of the extended lattice-lattice scaling hypothesis for the class of models under consideration.

KW - Corrections to scaling

KW - Fibonacci sequences

KW - Ising model

KW - Lattice-lattice scaling

KW - Painlevé functions

KW - Penrose tilings

KW - Scaling limit

KW - Wavevector-dependent susceptibility

KW - Z-invariance

UR - http://www.scopus.com/inward/record.url?scp=0037381867&partnerID=8YFLogxK

U2 - 10.1016/S0378-4371(02)01780-6

DO - 10.1016/S0378-4371(02)01780-6

M3 - Conference article

SN - 0378-4371

VL - 321

SP - 81

EP - 89

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-2

T2 - Statphys - Taiwan - 2002: Lattice Models and Complex Systems

Y2 - 26 May 2002 through 1 June 2002

ER -

Susceptibility calculations in periodic and quasiperiodic planar Ising models

Abstract

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