  The bare Coulomb interaction between two like-charges is repulsive. When
these charges are immersed in an electrolyte, the thermal fluctuations of the
ions turn the bare Coulomb interaction into an effective interaction between
the two charges. An interesting question arises: is it possible that the
effective interaction becomes attractive for like-charges? We will show how
this like-charge attraction phenomenon is indeed predicted in some one- and
two-dimensional models of Coulomb systems. Exact analytical results can be
obtained for these Coulomb systems models due to some connections that they
have with integrable field theories. We will explain the techniques that allow
obtaining exact results for the correlation functions between like-charge
particles and how, under certain circumstances, the natural repulsion
interaction shifts to being attractive. Although the technical details differ
for 1d or 2d systems, the physical cause of this phenomenon is rooted in a
three-body interaction between the two like-charges and an ion of the
electrolyte with an opposite charge.
