The two-dimensional Coulomb gas with logarithmic interaction is studied by Monte Carlo simulation. We find clear evidence for the existence of a phase transition without referring to any theory. The analysis relies on the duality between Coulomb gas and discrete Gaussian model. The transition point $T_c$ is in excellent agreement with the Kosterlitz theory. The correlation functions support the renormalization-group results and disagree with the mean-field results.

• Received 26 February 1980

DOI:https://doi.org/10.1103/PhysRevB.23.308