  In the conformal field theories given by the Ising and Dirac models, when the
system is in the ground state, the moments of the reduced density matrix of two
disjoint intervals and of its partial transpose have been written as partition
functions on higher genus Riemann surfaces with $\mathbb{Z}_n$ symmetry. We
show that these partition functions can be expressed as the grand canonical
partition functions of the two-dimensional two component classical Coulomb gas
on certain circular lattices at specific values of the coupling constant.
