Like-charge attraction at short distances in a charge-asymmetric two-dimensional two-component plasma: Exact results

We determine exactly the short-distance effective potential between two "guest" charges immersed in a two-dimensional two-component charge-asymmetric plasma composed of positively ($q_1 = +1$) and negatively ($q_2 = -1/2$) charged point particles. The result is valid over the whole regime of stability, where the Coulombic coupling (dimensionless inverse temperature) $\beta <4$. At high Coulombic coupling $\beta>2$, this model features like-charge attraction. Also, there cannot be repulsion between opposite-charges at short-distances, at variance with large-distance interactions.