# RKKY interaction in graphene at finite temperature

## TL;DR

This paper extends previous zero-temperature calculations of RKKY interaction in graphene to finite temperatures using Matsubara formalism, providing a more comprehensive understanding of magnetic impurity interactions in graphene.

## Contribution

It generalizes the earlier zero-temperature approach to finite temperatures, enabling more accurate modeling of magnetic interactions in graphene under realistic conditions.

## Key findings

- RKKY interaction can be calculated at finite temperature using the generalized approach.
- Finite temperature effects modify the strength and range of magnetic interactions.
- The method simplifies previous calculations by using Matsubara formalism.

## Abstract

In our publication from 8 years ago (Phys. Rev. B {\bf 84}, 115119 (2011)) we calculated RKKY interaction between two magnetic impurities adsorbed on graphene at zero temperature. We show in this short paper that the approach based on Matsubara formalism and perturbation theory for the thermodynamic potential in the imaginary time and coordinate representation which was used then, can be easily generalized, and calculate RKKY interaction between the magnetic impurities at finite temperature.