On the universality of anomalous one-dimensional heat conductivity

In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long–time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat transport in 1d crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with the system size $L$ as $\kappa \propto L^{\alpha }$. However, the exponent $\alpha$ deviates systematically from the theoretical prediction $\alpha =1\mathrm{/}3$ proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev. Lett. {\bf 89}, 200601 (2002)].