Heat current flows across an interface in two-dimensional lattices

Heat current J that flows through a few typical two-dimensional nonlinear lattices is systematically studied. Each lattice consists of two identical segments that are coupled by an interface with strength k_{int}. It is found that the two-universality-class scenario that is revealed in one-dimensional systems is still valid in the two-dimensional systems. Namely, J may follow k_{int} in two entirely different ways, depending on whether or not the interface potential energy decays to zero. We also study the dependence of J on lattice width N_{Y} and transverse interaction strength k_{Y}. Universal power-law decay or divergence is observed. Finally, we check the equipartition theorem in the systems since it is the basis of all our theoretical analyses. Surprisingly, it holds perfectly even at the interface where there is a finite temperature jump, which makes the system far from equilibrium. However, the equipartition of potential energy, which is observed in one-dimensional systems, is no longer satisfied due to the interaction between different dimensions.