Heat transport in a chain of α-XY rotators

The conduction of heat is one of the simplest
but at the same time most intriguing problems in non-equilibrium physics.
Its study has put into evidence transport anomalies for low dimensional systems.
In other words, in the thermodynamic limit, the Fourier's law is not satisfied for
low-dimensional systems. The conductivity shows a dependence on the size $N$ of the
system according to the form $\kappa \sim N^a$, where the value of $a$ is dependent
on the interaction potential. But there are controversies concerning its origin.
It has been argued that the momentum conservation is the responsible for a non-Fourier behavior,
however rotator systems have displayed normal heat transport.
On the other hand, it is known that the range of the interactions brings new phenomena to a system [1,2].
So, in this work, we investigate by means of molecular dynamics simulations the role that the interaction
range plays on the heat conductivity. For this purpose we consider a chain of rotators with
interactions that depend algebraically on the distance between rotators, with a parameter that
controls the range of the interactions [1]. We determine the critical range at which the systems
passes from a flat temperature profile (mean field) to a normal profile (first neighbors).

[1] Anteneodo \& Tsallis, PRL 80, 5313 (1998); Tamarit \& Anteneodo, PRL 82, 208 (2000)

[2] Moyano \& Anteneodo, PRE 74, 021118 (2006)