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 Tc is in excellent agreement with the Kosterlitz theory. The correlation functions support the renormalization-group results and disagree with the mean-field results.
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Saito et al. (1981) studied this question.
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