作者：Henrique Santos Lima Constantino Tsallis
通过分子动力学研究了铁磁性耦合平面旋转体$d=1$晶格的热导率。在惯性XY模型中假设了两种不同类型的各向异性（局部各向异性和耦合中的各向异性）。在极端各向异性的极限下，两种模型都接近伊辛模型，其热导率为$\kappa$，在高温下，其标度为$\κ\sim T^｛-3｝$。这种行为强化了在各种$d$维模型中获得的结果，即$\kappa\proto-L\，e_｛q｝^｛-B（L^｛\gamma｝T）^｛\eta｝｝$，其中$e_q^z\equiv[1+（1-q）z]^｛\frac｛1｝｛1-q｝｝｝\；（e_1^z=e^z）$，$L$是$d$维宏观晶格的线性大小。比例定律$\frac｛\eta\，\gamma｝｛q-1｝=1$保证了傅立叶定律$\对所有d$的有效性。
The thermal conductivity of a $d=1$ lattice of ferromagnetically coupledplanar rotators is studied through molecular dynamics. Two different types ofanisotropies (local and in the coupling) are assumed in the inertial XY model.In the limit of extreme anisotropy, both models approach the Ising model andits thermal conductivity $\kappa$, which, at high temperatures, scales like$\kappa\sim T^{-3}$. This behavior reinforces the result obtained in various$d$-dimensional models, namely $\kappa \propto L\,e_{q}^{-B(L^{\gamma}T)^{\eta}}$ where $e_q^z\equiv[1+(1-q)z]^{\frac{1}{1-q}}\;(e_1^z=e^z)$, $L$ being the linear size ofthe $d$-dimensional macroscopic lattice. The scaling law $\frac{\eta\,\gamma}{q-1}=1$ guarantees the validity of Fourier’s law, $\forall d$.
论文链接：http://arxiv.org/pdf/2303.13432v1
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