Thermal transport in low-dimensional lattices with nearest- and next-nearest-neighbour coupling

We examine the effect of increasing the range of interaction on the anomalous transport properties of classical low-dimensional lattices coupled to thermal baths at different temperatures. We consider one-dimensional next-nearest-neighbour (NNN) interactions as well as a zig-zag model of two chains with nonlinearity of Fermi-Pasta-Ulam (namely quartic + quadratic) type. As in the case of linear chains with nearest-neighbour coupling, the thermal conductivity diverges as a power of the system size. The characteristic exponents are, however, distinct, and appear to depend on the strength of the coupling