Heat conduction in two-dimensional nonlinear lattices

The divergence of the heat conductivity in the thermodynamic limit is inves tigated in 2d-lattice models of anharmonic solids with nearest-neighbour in teraction from single-well potentials. Two different numerical approaches b ased on nonequilibrium and equilibrium simulations protide consistent indic ations in favour of a logarithmic divergence in "ergodic", i.e., highly cha otic, dynamical regimes. Analytical estimates obtained in thr framework of linear-responce theory confirm this finding, while tracing back the physica l origin of this anomalous transport to the slow diffusion of the energy of hydrodynamic modes, finally, numerical evidence of superanomalous transpor t is given in the weakly chaotic regime, typically observed below a thresho ld value of the energy density.