Recent progress in global-balance Monte Carlo algorithms has allowed to confirm the essentials of the Halperin-Nelson-Young theory (KTHNY) for the 2D Melting problem with short-range interactions [1]. A key challenge in these simulations are large correlation lengths which could be overcome by a new class of Monte Carlo algorithms [2].
In this talk, I will show that the new Monte Carlo paradigm can be extended to include long-range forces (including periodic images) rigorously, without any truncation effects. The resulting algorithm improves on the scaling of Ewald summation [3].

The new algorithm allows to check the scaling predictions of KTHNY theory in the long-range limit, and complete the phase diagram of inverted power-law potentials, relevant for charged colloids, plasma crystals, and other systems.

[1] S. C. Kapfer & W. Krauth, Phys. Rev. Lett. 114, 035702 (2015).

[2] M. Michel et al., J. Chem. Phys. 140, 054116 (2014).

[3] S. C. Kapfer & W. Krauth, Phys. Rev. E 94 (R), 031302 (2016).