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A nonconventional renormalization-group (RG) treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their quantum critical point. The approach consists in a preliminary averaging over quantum degrees of freedom and a successive employment of the Wilsonian RG transformation to treat the resulting effective classical Ginzburg-Landau free energy functional. This allows us to perform a detailed study of criticality of the quantum systems under study. The emergent physics agrees, in many aspects, with the known quantum critical scenario. However, a richer structure of the phase diagram appears with additional crossovers which are not captured by the traditional RG studies. In addition, in spite of the intrinsically static nature of our theory, predictions about the dynamical critical exponent, which parametrizes the link between statics and dynamics close to a continuous phase transition, are consistently derived from our static results.
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an unstable cri
We revisit the two-dimensional quantum Ising model by computing renormalization group flows close to its quantum critical point. The low but finite temperature regime in the vicinity of the quantum critical point is squashed between two distinct non-
We present mathematical details of derivation of the critical exponents for the free energy and magnetization in the vicinity of the Gaussian fixed point of renormalization. We treat the problem in general terms and do not refer to particular models
We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent $alpha$, in regimes of direct interest for current trapped ion experiments. Using larg
We show that the synchronization transition of a large number of noisy coupled oscillators is an example for a dynamic critical point far from thermodynamic equilibrium. The universal behaviors of such critical oscillators, arranged on a lattice in a