Heat current properties of a rotor chain type model with next-nearest-neighbor interactions

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In this article, to study the heat flow behavior, we perform analytical investigations in a rotor chain type model (involving inner stochastic noises) with next and next-nearest-neighbor (NN) interactions. It is known in the literature that the chain rotor model with long range interactions presents an insulating phase for the heat conductivity. But we show, in contrast with such a behavior, that the addition of a next-NN potential increases the thermal conductivity, at least in the low temperature regime, indicating that the insulating property is a genuine long range interaction effect. We still establish, now by numerical computations, the existence of a thermal rectification in systems with graded structures.