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We use first-principles quantum Monte Carlo simulations to study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between hydrogen adatoms attached to a graphene sheet. We find that the pairwise RKKY interactions at distances of a few lattice spacings are strongly affected by interelectron interactions, in particular, the potential barrier between widely separated adatoms and the dimer configuration becomes wider and thus harder to penetrate. We also point out that antiferrromagnetic and charge density wave orderings have very different effects on the RKKY interaction. Finally, we analyze the stability of several regular adatom superlattices with respect to small displacements of a single adatom, distinguishing the cases of adatoms which populate either both or only one sublattice of the graphene lattice. [ABSTRACT FROM AUTHOR]

We report on Hybrid Monte Carlo simulations at finite spin density of the π-band electrons in monolayer graphene with realistic interelectron interactions. Unlike simulations at finite charge-carrier density, these are not affected by a fermion-sign problem. Our results are in qualitative agreement with an interaction-induced warping of the Fermi contours and a reduction of the bandwidth as observed in angle-resolved photoemission spectroscopy experiments on charge-doped graphene systems. Furthermore, we find evidence that the neck-disrupting Lifshitz transition, which occurs when the Fermi level traverses the van Hove singularity (VHS), becomes a true quantum phase transition due to interactions. This is in line with an instability of the VHS toward the formation of ordered electronic phases, which has been predicted by a variety of different theoretical approaches. [ABSTRACT FROM AUTHOR]

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called "slow mode," which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for the Ising model and the linear-log-relaxation (LLR) method as simulation algorithm. We first demonstrate supercritical slowing down in a phase with spontaneously broken symmetry and for the heat-bath algorithms, for which autocorrelation times grow exponentially with system size. By contrast, using the magnetization as collective coordinate, we present evidence that supercritical slowing down is absent. We still observe a polynomial increase of the autocorrelation time with volume (critical slowing down), which is, however, reduced by orders of magnitude when compared to local update techniques.