### Abstract

We show that the statistical mechanics of Ising models can be conveniently reformulated in terms of the local magnetic field probability distribution function P(h). It is shown that for arbitrary exchange interactions Jij, which may or may not be random, both thermodynamic quantities such as magnetization, specific heat, etc., and the neutron scattering law S(k,) can be obtained from P(h). Indeed S(k,) provides a direct measurement of the symmetric part of P(h) which also determines the energy, specific heat, etc., while the magnetization can be obtained from the antisymmetric part of P(h). As an example, specific results for P(h) are presented for the honeycomb, square, and triangular lattices with constant nearest-neighbor interactions. All three lattices exhibit a pronounced dip in the center of P(h) at the transition temperature.

Original language | English (US) |
---|---|

Pages (from-to) | 250-258 |

Number of pages | 9 |

Journal | Physical Review B |

Volume | 30 |

Issue number | 1 |

DOIs | |

State | Published - 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*30*(1), 250-258. https://doi.org/10.1103/PhysRevB.30.250

**Local magnetic field distributions : Two-dimensional Ising models.** / Thomsen, M.; Thorpe, Michael; Choy, T. C.; Sherrington, D.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 30, no. 1, pp. 250-258. https://doi.org/10.1103/PhysRevB.30.250

}

TY - JOUR

T1 - Local magnetic field distributions

T2 - Two-dimensional Ising models

AU - Thomsen, M.

AU - Thorpe, Michael

AU - Choy, T. C.

AU - Sherrington, D.

PY - 1984

Y1 - 1984

N2 - We show that the statistical mechanics of Ising models can be conveniently reformulated in terms of the local magnetic field probability distribution function P(h). It is shown that for arbitrary exchange interactions Jij, which may or may not be random, both thermodynamic quantities such as magnetization, specific heat, etc., and the neutron scattering law S(k,) can be obtained from P(h). Indeed S(k,) provides a direct measurement of the symmetric part of P(h) which also determines the energy, specific heat, etc., while the magnetization can be obtained from the antisymmetric part of P(h). As an example, specific results for P(h) are presented for the honeycomb, square, and triangular lattices with constant nearest-neighbor interactions. All three lattices exhibit a pronounced dip in the center of P(h) at the transition temperature.

AB - We show that the statistical mechanics of Ising models can be conveniently reformulated in terms of the local magnetic field probability distribution function P(h). It is shown that for arbitrary exchange interactions Jij, which may or may not be random, both thermodynamic quantities such as magnetization, specific heat, etc., and the neutron scattering law S(k,) can be obtained from P(h). Indeed S(k,) provides a direct measurement of the symmetric part of P(h) which also determines the energy, specific heat, etc., while the magnetization can be obtained from the antisymmetric part of P(h). As an example, specific results for P(h) are presented for the honeycomb, square, and triangular lattices with constant nearest-neighbor interactions. All three lattices exhibit a pronounced dip in the center of P(h) at the transition temperature.

UR - http://www.scopus.com/inward/record.url?scp=4243712136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243712136&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.30.250

DO - 10.1103/PhysRevB.30.250

M3 - Article

AN - SCOPUS:4243712136

VL - 30

SP - 250

EP - 258

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 1

ER -