We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.Comment: 6 pages, 5 figure

The one-dimensional periodic Anderson model with an additional Coulomb repulsion U fc between localized f and conduction electrons has been investigated using the projector-based renormalization method. Due to the presence of U fc and the hybridization V between localized and conduction electrons, various gaps are found in the quasiparticle dispersion k . The number of gaps depends on the density of the localized electrons. Moreover, a valence transition from an integer to a mixed f valence is found as a function of the bare f level energy f . Its dependence on various model parameters is investigated for fixed total electron density. In particular, the transition is sharpened either by increasing U fc or by decreasing the hybridization or the temperature.