Magnetic responses in the presence of a partial magnetic field on the rectangular Ising lattice

Shu Chiuan Chang, Masuo Suzuki

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study the two-dimensional Ising model for the square lattice in the presence of a magnetic field which applies on a part of spins. Specifically, we consider the situation in which only the spins on a row or a diagonal line can interact with the magnetic field. The low-temperature series expansions of the reduced partition functions for the square lattice with a magnetic field on a row are presented for both ferromagnetic and antiferromagnetic spin-spin couplings. The low- and high-temperature series expansions of the zero-field susceptibility for the above lattice are performed, and the critical amplitudes are estimated. The critical exponent γ′r of the susceptibility for a ferromagnet is confirmed to be 3/4. The spontaneous magnetization per field-applied site of the same system is found to be the same as the ordinary spontaneous magnetization per site with an uniform magnetic field. The exact partition functions are also obtained for the super-exchange model applying both on a boundary row and on the central row of the rectangular Ising lattice.

Original languageEnglish
Pages (from-to)299-332
Number of pages34
JournalPhysica A: Statistical Mechanics and its Applications
Volume341
Issue number1-4
DOIs
Publication statusPublished - 2004 Oct 1

Fingerprint

Ising
Magnetic Field
Partial
series expansion
Series Expansion
Square Lattice
magnetic fields
Partition Function
Magnetization
Susceptibility
partitions
High Temperature Expansion
magnetic permeability
magnetization
spin-spin coupling
Ferromagnet
Critical Exponents
Ising model
Ising Model
exponents

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

@article{26a80f79b1c0402d8bdcd1e6a00c78f8,
title = "Magnetic responses in the presence of a partial magnetic field on the rectangular Ising lattice",
abstract = "We study the two-dimensional Ising model for the square lattice in the presence of a magnetic field which applies on a part of spins. Specifically, we consider the situation in which only the spins on a row or a diagonal line can interact with the magnetic field. The low-temperature series expansions of the reduced partition functions for the square lattice with a magnetic field on a row are presented for both ferromagnetic and antiferromagnetic spin-spin couplings. The low- and high-temperature series expansions of the zero-field susceptibility for the above lattice are performed, and the critical amplitudes are estimated. The critical exponent γ′r of the susceptibility for a ferromagnet is confirmed to be 3/4. The spontaneous magnetization per field-applied site of the same system is found to be the same as the ordinary spontaneous magnetization per site with an uniform magnetic field. The exact partition functions are also obtained for the super-exchange model applying both on a boundary row and on the central row of the rectangular Ising lattice.",
author = "Chang, {Shu Chiuan} and Masuo Suzuki",
year = "2004",
month = "10",
day = "1",
doi = "10.1016/j.physa.2004.04.131",
language = "English",
volume = "341",
pages = "299--332",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "1-4",

}

Magnetic responses in the presence of a partial magnetic field on the rectangular Ising lattice. / Chang, Shu Chiuan; Suzuki, Masuo.

In: Physica A: Statistical Mechanics and its Applications, Vol. 341, No. 1-4, 01.10.2004, p. 299-332.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Magnetic responses in the presence of a partial magnetic field on the rectangular Ising lattice

AU - Chang, Shu Chiuan

AU - Suzuki, Masuo

PY - 2004/10/1

Y1 - 2004/10/1

N2 - We study the two-dimensional Ising model for the square lattice in the presence of a magnetic field which applies on a part of spins. Specifically, we consider the situation in which only the spins on a row or a diagonal line can interact with the magnetic field. The low-temperature series expansions of the reduced partition functions for the square lattice with a magnetic field on a row are presented for both ferromagnetic and antiferromagnetic spin-spin couplings. The low- and high-temperature series expansions of the zero-field susceptibility for the above lattice are performed, and the critical amplitudes are estimated. The critical exponent γ′r of the susceptibility for a ferromagnet is confirmed to be 3/4. The spontaneous magnetization per field-applied site of the same system is found to be the same as the ordinary spontaneous magnetization per site with an uniform magnetic field. The exact partition functions are also obtained for the super-exchange model applying both on a boundary row and on the central row of the rectangular Ising lattice.

AB - We study the two-dimensional Ising model for the square lattice in the presence of a magnetic field which applies on a part of spins. Specifically, we consider the situation in which only the spins on a row or a diagonal line can interact with the magnetic field. The low-temperature series expansions of the reduced partition functions for the square lattice with a magnetic field on a row are presented for both ferromagnetic and antiferromagnetic spin-spin couplings. The low- and high-temperature series expansions of the zero-field susceptibility for the above lattice are performed, and the critical amplitudes are estimated. The critical exponent γ′r of the susceptibility for a ferromagnet is confirmed to be 3/4. The spontaneous magnetization per field-applied site of the same system is found to be the same as the ordinary spontaneous magnetization per site with an uniform magnetic field. The exact partition functions are also obtained for the super-exchange model applying both on a boundary row and on the central row of the rectangular Ising lattice.

UR - http://www.scopus.com/inward/record.url?scp=3343020134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3343020134&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2004.04.131

DO - 10.1016/j.physa.2004.04.131

M3 - Article

AN - SCOPUS:3343020134

VL - 341

SP - 299

EP - 332

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-4

ER -