Dimensional crossover of heat conduction in low dimensions

The dimensional crossover phenomena of heat conduction is studied by a two-dimensional (2D) Fermi-Pasta-Ulam lattice. The 2D divergence law of the thermal conductivity is confirmed by the simulations results. The divergence law of the thermal conductivity will change from the 2D class to 1D class as δ= N/ Nx decreases, here Ny is the size in transverse direction and Nx in longitude direction. The simulation's results suggest that the dimensional crossover happens in δ* →0 as Nx →.