Exact spin–spin correlation function for the zero-temperature random-field Ising model

P. Handford, Francisco J. Perez-Reche, Sergei N. Taraskin

Research output: Contribution to journal › Article

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Abstract

An exact expression for the spin–spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin–spin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.
Original languageEnglish
Article numberP01001
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2012
DOIs
Publication statusPublished - Jan 2012
Externally publishedYes

Fingerprint

Bethe Lattice
Correlation Length
Temperature Field
Random Field
Ising model
Ising Model
Correlation Function
Critical Dimension
Zero
Diverge
Length Scale
Mean Field
Critical Exponents
Critical point
Power Law
temperature
Arbitrary
coordination number
critical point
exponents

Cite this

Handford, P. ; Perez-Reche, Francisco J. ; Taraskin, Sergei N. / Exact spin–spin correlation function for the zero-temperature random-field Ising model. In: Journal of Statistical Mechanics: Theory and Experiment. 2012 ; Vol. 2012.
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abstract = "An exact expression for the spin–spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin–spin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.",
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Handford, P, Perez-Reche, FJ & Taraskin, SN 2012, 'Exact spin–spin correlation function for the zero-temperature random-field Ising model', Journal of Statistical Mechanics: Theory and Experiment, vol. 2012, P01001. https://doi.org/10.1088/1742-5468/2012/01/P01001

Exact spin–spin correlation function for the zero-temperature random-field Ising model. / Handford, P.; Perez-Reche, Francisco J.; Taraskin, Sergei N.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, P01001, 01.2012.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Exact spin–spin correlation function for the zero-temperature random-field Ising model

AU - Handford, P.

AU - Perez-Reche, Francisco J.

AU - Taraskin, Sergei N.

PY - 2012/1

Y1 - 2012/1

N2 - An exact expression for the spin–spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin–spin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.

AB - An exact expression for the spin–spin correlation function is derived for the zero-temperature random-field Ising model defined on a Bethe lattice of arbitrary coordination number. The correlation length describing dynamic spin–spin correlations and separated from the intrinsic topological length scale of the Bethe lattice is shown to diverge as a power law at the critical point. The critical exponents governing the behaviour of the correlation length are consistent with the mean-field values found for a hypercubic lattice with dimension greater than the upper critical dimension.

U2 - 10.1088/1742-5468/2012/01/P01001

DO - 10.1088/1742-5468/2012/01/P01001

M3 - Article

VL - 2012

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

M1 - P01001

ER -

Handford P, Perez-Reche FJ, Taraskin SN. Exact spin–spin correlation function for the zero-temperature random-field Ising model. Journal of Statistical Mechanics: Theory and Experiment. 2012 Jan;2012. P01001. https://doi.org/10.1088/1742-5468/2012/01/P01001

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