Maxwell field \( \mathbf{E}\) in a two-dimensional polar fluid in the presence of an external field \(\boldsymbol{\mathcal{E}} \) : a Monte-Carlo study

We study a two-dimensional system of dipolar hard disks in the presence of a uniform external electric field \(\boldsymbol{\mathcal{E}} \) by Monte Carlo simulations in a square with periodic boundary conditions. The study is performed in both the fluid at high temperature and the phase of living polymers at low temperature. In the considered geometry the macroscopic Maxwell field \( \mathbf{E}\) is computed and found to be equal to the external field \(\boldsymbol{\mathcal{E}} \) in both phases. The dielectric properties of the system in the liquid phase as well as in the polymeric phase are investigated.