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

Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice