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Ising chain: Thermal conductivity and first-principle validation of Fourier’s law

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  • Lima, Henrique Santos
  • Tsallis, Constantino

Abstract

The thermal conductivity of a d=1 lattice of ferromagnetically coupled planar rotators is studied through molecular dynamics. Two different types of anisotropies (local and in the coupling) are assumed in the inertial XY model. In the limit of extreme anisotropy, both models approach the Ising model and its thermal conductivity κ, which, at high temperatures, scales like κ∼T−3. This behavior reinforces the result obtained in various d-dimensional models, namely κ∝Leq−B(LγT)η where eqz≡[1+(1−q)z]11−q(e1z=ez), L being the linear size of the d-dimensional macroscopic lattice. The scaling law ηγq−1=1 guarantees the validity of Fourier’s law, for all dimensions.

Suggested Citation

  • Lima, Henrique Santos & Tsallis, Constantino, 2023. "Ising chain: Thermal conductivity and first-principle validation of Fourier’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    • Handle: RePEc:eee:phsmap:v:628:y:2023:i:c:s0378437123007161
    DOI: 10.1016/j.physa.2023.129161
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    References listed on IDEAS

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    1. Gruber, Christian & Lesne, Annick, 2005. "Hamiltonian model of heat conductivity and Fourier law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 358-372.
    2. Yunyun Li & Nianbei Li & Baowen Li, 2015. "Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(7), pages 1-6, July.
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