Spontaneous Magnetization of the square 2D Ising lattice with nearest- and weak next-nearest neighbour interactions

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Abstract

We show that the square two-dimensional (2D) Ising lattice with nearest- (J) and weak next-nearest-neighbour interactions (Jd) can be mapped on a square 2D Ising lattice that has only nearest neighbour interactions (J*). For Jd/J << 1 the transformation equation has the simple form GPHT_A_361184_O_XML_IMAGES\GPHT_A_361184_O_ILM0001.gif. This result can be used to derive expressions for several thermodynamic functions of the square 2D Ising lattice with weak next-nearest-neighbour interactions. As an example we consider the spontaneous magnetization and compare it with low-temperature series expansion results.
Original languageUndefined
Pages (from-to)191-196
Number of pages6
JournalPhase transitions
Volume82
Issue number2
DOIs
Publication statusPublished - 2009

Keywords

  • METIS-251379
  • IR-73021

Cite this

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title = "Spontaneous Magnetization of the square 2D Ising lattice with nearest- and weak next-nearest neighbour interactions",
abstract = "We show that the square two-dimensional (2D) Ising lattice with nearest- (J) and weak next-nearest-neighbour interactions (Jd) can be mapped on a square 2D Ising lattice that has only nearest neighbour interactions (J*). For Jd/J << 1 the transformation equation has the simple form GPHT_A_361184_O_XML_IMAGES\GPHT_A_361184_O_ILM0001.gif. This result can be used to derive expressions for several thermodynamic functions of the square 2D Ising lattice with weak next-nearest-neighbour interactions. As an example we consider the spontaneous magnetization and compare it with low-temperature series expansion results.",
keywords = "METIS-251379, IR-73021",
author = "Zandvliet, {Henricus J.W.} and C. Hoede",
note = "Open Access",
year = "2009",
doi = "10.1080/01411590802610163",
language = "Undefined",
volume = "82",
pages = "191--196",
journal = "Phase transitions",
issn = "0141-1594",
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}

Spontaneous Magnetization of the square 2D Ising lattice with nearest- and weak next-nearest neighbour interactions. / Zandvliet, Henricus J.W.; Hoede, C.

In: Phase transitions, Vol. 82, No. 2, 2009, p. 191-196.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Spontaneous Magnetization of the square 2D Ising lattice with nearest- and weak next-nearest neighbour interactions

AU - Zandvliet, Henricus J.W.

AU - Hoede, C.

N1 - Open Access

PY - 2009

Y1 - 2009

N2 - We show that the square two-dimensional (2D) Ising lattice with nearest- (J) and weak next-nearest-neighbour interactions (Jd) can be mapped on a square 2D Ising lattice that has only nearest neighbour interactions (J*). For Jd/J << 1 the transformation equation has the simple form GPHT_A_361184_O_XML_IMAGES\GPHT_A_361184_O_ILM0001.gif. This result can be used to derive expressions for several thermodynamic functions of the square 2D Ising lattice with weak next-nearest-neighbour interactions. As an example we consider the spontaneous magnetization and compare it with low-temperature series expansion results.

AB - We show that the square two-dimensional (2D) Ising lattice with nearest- (J) and weak next-nearest-neighbour interactions (Jd) can be mapped on a square 2D Ising lattice that has only nearest neighbour interactions (J*). For Jd/J << 1 the transformation equation has the simple form GPHT_A_361184_O_XML_IMAGES\GPHT_A_361184_O_ILM0001.gif. This result can be used to derive expressions for several thermodynamic functions of the square 2D Ising lattice with weak next-nearest-neighbour interactions. As an example we consider the spontaneous magnetization and compare it with low-temperature series expansion results.

KW - METIS-251379

KW - IR-73021

U2 - 10.1080/01411590802610163

DO - 10.1080/01411590802610163

M3 - Article

VL - 82

SP - 191

EP - 196

JO - Phase transitions

JF - Phase transitions

SN - 0141-1594

IS - 2

ER -