[en] In this thesis I aim to investigate ground-state properties of a quantum-mechanical longrange interacting spin model at temperature T = 0 K. Paradigmatic models such as the Ising model are mostly limited to nearest-neighbor interactions. However, their long-range counterparts often display a drastically different behavior. Long-range interactions can induce an effective dimensionality into the system, leading to continuously varying critical exponents of quantum phase transitions in ferromagnetic systems and the appearance of multiplicative logarithmic corrections. For antiferromagnetic interactions frustration can result in the appearance of new phases. During the last decades several studies of such models have been performed with various methods. Exact diagonalization and Quantum Monte-Carlo calculations are yet limited to finite system sizes. Density-matrix renormalization-group methods allow handling infinite sizes but results are only available for (quasi-)one-dimensional models. In this thesis, a method is presented which allows the computation of quantitative results for gapped quantum-many-body systems with long-range interactions in the bulk limit based on a perturbative approach. Perturbative continuous unitary transformations are combined with Monte-Carlo methods for an evaluation of nested infinite sums and Padé extrapolations to extract critical behavior. Long-range-interacting Ising models in a transverse magnetic field were analyzed, where the interaction decays algebraically as r${}^{-<!--\; ???\; -->\mathrm{\alpha <!--\; ??\; -->}}$ with inter-spin distance r. The investigation of low-energy excitation gaps was used to determine phase diagrams and critical exponents for multiple different lattice geometries. For ferromagnetic spin-spin interactions a phase transition from a polarized paramagnetic phase in the high-field limit to an ordered phase, which breaks the ${\mathbb{Z}}^2$ symmetry, was found in all cases. Depending on $\mathrm{\alpha <!--\; ??\; -->}$ renormalization-group calculations predict three different regimes. For small $\mathrm{\alpha <!--\; ??\; -->}$ mean-field criticality is expected while for large values systems are supposed to display nearest-neighbor exponents. Continuously-varying critical exponents that are expected to exist in between could be confirmed in this thesis. In one and two dimensions multiplicative logarithmic corrections were found that are expected for the nearest-neighbor model only on the cubic lattice in three dimensions. This strengthens the interpretation of the long-range model as having similar properties as the short-range-interacting model in an effective dimension. While in this thesis frustration effects induced by an antiferromagnetic interaction were already found for bipartite lattices, these are especially interesting for models that are already highly frustrated in the nearest-neighbor case. For the Ising model on the triangular lattice additional stripe-ordered phases were found, leading to an increased complexity of the ground-state phase diagram. After mapping the triangular lattice to a finite cylinder, indications for infinite-order phase transitions appeared that require further studies in the future.