The 2D Ising square lattice with nearest- and next-nearest-neighbor interactions

Research output: Contribution to journalArticleAcademicpeer-review

31 Citations (Scopus)

Abstract

An analytical expression for the boundary free energy of the Ising square lattice with nearest- and next-nearest-neighbor interactions is derived. The Ising square lattice with anisotropic nearest-neighbor (Jx and Jy) and isotropic next-nearest-neighbor (Jd) interactions has an order-disorder phase transition at a temperature T = Tc given by the condition e−2Jx/kbTc + e− 2Jy/kbTc + e−2(Jx + Jy)/kbTc(2 − e−4Jd/kbTc) = e4Jd/kbTc. The critical line that separates the ordered (ferromagnetic) phase from the disordered (paramagnetic) phase is in excellent agreement with series expansion, finite scaling of transfer matrix and Monte Carlo results. For a vanishing next-nearest-neighbor interaction Onsager's famous result, i.e. sinh (2Jx/kbTc)sinh (2Jy/kbTc) = 1, is recaptured.
Original languageUndefined
Pages (from-to)747-751
Number of pages4
JournalEurophysics letters
Volume73
Issue number5
DOIs
Publication statusPublished - 2006

Keywords

  • METIS-232785
  • IR-61315

Cite this

@article{1f6a46fc311046b787fb71dd52f6524c,
title = "The 2D Ising square lattice with nearest- and next-nearest-neighbor interactions",
abstract = "An analytical expression for the boundary free energy of the Ising square lattice with nearest- and next-nearest-neighbor interactions is derived. The Ising square lattice with anisotropic nearest-neighbor (Jx and Jy) and isotropic next-nearest-neighbor (Jd) interactions has an order-disorder phase transition at a temperature T = Tc given by the condition e−2Jx/kbTc + e− 2Jy/kbTc + e−2(Jx + Jy)/kbTc(2 − e−4Jd/kbTc) = e4Jd/kbTc. The critical line that separates the ordered (ferromagnetic) phase from the disordered (paramagnetic) phase is in excellent agreement with series expansion, finite scaling of transfer matrix and Monte Carlo results. For a vanishing next-nearest-neighbor interaction Onsager's famous result, i.e. sinh (2Jx/kbTc)sinh (2Jy/kbTc) = 1, is recaptured.",
keywords = "METIS-232785, IR-61315",
author = "Zandvliet, {Henricus J.W.}",
year = "2006",
doi = "10.1209/epl/i2005-10451-1",
language = "Undefined",
volume = "73",
pages = "747--751",
journal = "Europhysics letters",
issn = "0295-5075",
publisher = "IOP Publishing Ltd.",
number = "5",

}

The 2D Ising square lattice with nearest- and next-nearest-neighbor interactions. / Zandvliet, Henricus J.W.

In: Europhysics letters, Vol. 73, No. 5, 2006, p. 747-751.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - The 2D Ising square lattice with nearest- and next-nearest-neighbor interactions

AU - Zandvliet, Henricus J.W.

PY - 2006

Y1 - 2006

N2 - An analytical expression for the boundary free energy of the Ising square lattice with nearest- and next-nearest-neighbor interactions is derived. The Ising square lattice with anisotropic nearest-neighbor (Jx and Jy) and isotropic next-nearest-neighbor (Jd) interactions has an order-disorder phase transition at a temperature T = Tc given by the condition e−2Jx/kbTc + e− 2Jy/kbTc + e−2(Jx + Jy)/kbTc(2 − e−4Jd/kbTc) = e4Jd/kbTc. The critical line that separates the ordered (ferromagnetic) phase from the disordered (paramagnetic) phase is in excellent agreement with series expansion, finite scaling of transfer matrix and Monte Carlo results. For a vanishing next-nearest-neighbor interaction Onsager's famous result, i.e. sinh (2Jx/kbTc)sinh (2Jy/kbTc) = 1, is recaptured.

AB - An analytical expression for the boundary free energy of the Ising square lattice with nearest- and next-nearest-neighbor interactions is derived. The Ising square lattice with anisotropic nearest-neighbor (Jx and Jy) and isotropic next-nearest-neighbor (Jd) interactions has an order-disorder phase transition at a temperature T = Tc given by the condition e−2Jx/kbTc + e− 2Jy/kbTc + e−2(Jx + Jy)/kbTc(2 − e−4Jd/kbTc) = e4Jd/kbTc. The critical line that separates the ordered (ferromagnetic) phase from the disordered (paramagnetic) phase is in excellent agreement with series expansion, finite scaling of transfer matrix and Monte Carlo results. For a vanishing next-nearest-neighbor interaction Onsager's famous result, i.e. sinh (2Jx/kbTc)sinh (2Jy/kbTc) = 1, is recaptured.

KW - METIS-232785

KW - IR-61315

U2 - 10.1209/epl/i2005-10451-1

DO - 10.1209/epl/i2005-10451-1

M3 - Article

VL - 73

SP - 747

EP - 751

JO - Europhysics letters

JF - Europhysics letters

SN - 0295-5075

IS - 5

ER -