Renormalization Group and Critical Exponents for a Two‐Dimensional Ising Ferromagnet with Long‐Range Interaction

Lu, S. Fakio

doi:10.1002/pssb.2221090163

Physica Status Solidi (b)

1982

DOI: 10.1002/pssb.2221090163

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Renormalization Group and Critical Exponents for a Two‐Dimensional Ising Ferromagnet with Long‐Range Interaction

S. Fakio Lu

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1985

1989

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Cited by 3 publications

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Spin Anisotropy and Critical Exponents for a Heisenberg System A Renormalization Group Approach

1985

Physica Status Solidi (b)

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Firstly the renormalization group technique is applied to an isotropicHeisenberg spin system with long-range interaction and a set of critical exponents are calculated. These exponents are expressed in terms of a potential parameter u. All critical exponents except p, the magnetization exponent, depend on u. Secondly, the anisotropy is considered and the related croesover exponent p is evaluated. This later parameter turns out t o be equal to y, the susceptibility exponent, as predicted by some authors.Zuerst wird die Technik der Renormierungsgruppe auf das isotrope Heisenberg-Spin-System mit langreichweitiger Wechselwirkung angewandt und eine Reihe kritiecher Exponenten berechnet. Diese kritischen Exponenten werden in Abhangigkeit von dem Potential-Reichweite-Parameter u ausgedriickt. Alle kritjschen Exponenten au5er dem ExFonenten /? derMagnetisierung hiingen von (r ab. Dann wird diespinanisotropie einbezogen und der dazugehorige Sprung-Exponent (crossover exponent) bestimmt. Dieser Exponent ist gleich dem Suszeptibilitats-Exponent y, wie bereits vorausgesagt w urde .

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Spin Anisotropy and Critical Exponents for a Heisenberg System A Renormalization Group Approach

1985

Physica Status Solidi (b)

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Eigenvalues and Eigenfunctions of Renormalization Group Equations for Susceptibilities and Magnetizations

Fakioǧlu¹

1989

Physica Status Solidi (b)

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IntroductionHeisenberg models, one encounters great difficulties to solve them in the general framework of statistical and solid state physics. The critical structure of some systems is worth studying. These critical behaviours a r e well described by critical exponents /1/ near the critical point. In the following sections we write the eigenvalue equation of susceptibility and magnetization for a one-dimensional model obtained by the renormalization group approach and solve them in details. The nature of these equations, of course, depends on the mathematical models in hand as well as the assumed interaction po-

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Critical exponents for two-dimensional Heisenberg ferromagnet with long-range interaction

Fakioǧlu

1988

Il Nuovo Cimento D

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Renormalization Group and Critical Exponents for a Two‐Dimensional Ising Ferromagnet with Long‐Range Interaction

Cited by 3 publications

References 6 publications

Spin Anisotropy and Critical Exponents for a Heisenberg System A Renormalization Group Approach

Spin Anisotropy and Critical Exponents for a Heisenberg System A Renormalization Group Approach

Eigenvalues and Eigenfunctions of Renormalization Group Equations for Susceptibilities and Magnetizations

Critical exponents for two-dimensional Heisenberg ferromagnet with long-range interaction

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