Lima, Henrique Santos and Constantino Tsallis
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 K, which, at high temperatures, scales like K similar to T-3. This behavior reinforces the result obtained in various d-dimensional models, namely K proportional to Le-B(L gamma T)eta 1 qwhere ez 1-q(ez q equivalent to [1 + (1 - q)z] 1 = ez), L being the linear size of the d-dimensional macroscopic lattice. The scaling law eta gamma q-1= 1 guarantees the validity of Fourier's law, for all dimensions.