In this talk, I will argue that Cooper pairs can induce magnetic frustration in systems of two-dimensional (2D) magnetic adatom lattices on s-wave superconducting surfaces. The competition between singlet electron correlations and the RKKY coupling is shown to lead to a variety of hidden order states that break the point-group symmetry of the 2D adatom lattice at finite temperature. Using a newly developed effective bond theory [1, 2], we have constructed the corresponding phase diagram, which displays broad regions of long-range vestigial nematic order.
 M. Schecter, O. F. Syljuåsen, J. Paaske, Phys. Rev. Lett. 119, 157202 (2017)
 M. Schecter, O. F. Syljuåsen, J. Paaske, arXiv:1710.08439