Roughening behavior of a one-dimensional crystal surface with inverse square potential

The discrete Gaussian chain with inverse square potential—which models a one-dimensional crystal surface—is studied by Monte-Carlo methods. The system is found to undergo a roughening transition, and the temperature-dependent correlation function exponent η(T) is shown to be discontinous at the critical point. These results can be transposed to the metal-insulator transition of a one-dimensional plasma of logarithmically interacting charges.