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

Henrique Santos Lima and Constantino Tsallis

Physica A: Statistical Mechanics and its Applications, 2023, vol. 628, issue C

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.

Keywords: Nonextensive statistical mechanics; Langevin dynamics; Linear transport phenomena; Irreversibility (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:628:y:2023:i:c:s0378437123007161

DOI: 10.1016/j.physa.2023.129161

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