I. Rabuffo

Renormalization group and quantum critical phenomena in the large-n limit

The paper is devoted to a sistematic study of the critical behaviour and quantum regime of a wide class of quantum systems on the basis of the Renormalization Group (RG) approach in the large-n limit. It can be considered as a complement to recent perturbative (RG) investigations for the same systems and as a convenient basis for a treatment of the classical-quantum crossover. The differences between “Bosonized systems” and several quantum systems for which a dimensional crossover occurs in the low temperature limit are emphasized, consistently with the perturbative results and a calculation of the quantum non linear scaling field is also realized. Finally, a differential formulation of the quantum RG in the large-n limit is presented and its convenience in investigating some aspects of the problem is pointed out.

Temperature-dependent scaling fields and quantum criticality within the Wilson renormalization group approach

Within the Wilson Renormalization Group (WRG) approach as applied to d-dimensional quantum systems using appropriate functional representations, we develop a general method for describing the critical behaviour driven by the temperature T when the quantum fluctuations are into play. It consists in solving the quantum RG equations near a zero-temperature fixed point (FP) introducing T-dependent scaling fields which are determined by ordinary first-order differential equations with appropriate boundary conditions. This allows us to explore, in a unified and relatively simple way, the low-temperature properties near a (T = 0)-quantum instability of a great variety of quantum systems (interacting Bose gas, quantum ferroelectrics, itinerant fermion materials, spin models in a tranverse field, granular superconductors, etc.). The crossover from the low-but finite-temperature critical behaviour to the quantum criticality is also described in a natural way in terms of appropriate effective exponents. The predictions appear to be quite quantum systems by means of different approaches. For the interacting Bose gas and other quantum systems lying in the same universality class (bosonic systems), our results give us the opportunity to rexamine some uncorrect calculations for d ≤2 recently appeared in the literature.

Low-temperature quantum critical behaviour of systems with transverse Ising-like intrinsic dynamics

The low-temperature properties and crossover phenomena of d-dimensional transverse Ising-like systems within the influence domain of the quantum critical point are investigated solving the appropriate one-loop renormalization group equations. The phase diagram is obtained near and at d=3 and several sets of critical exponents are determined which describe different responses of a system to quantum fluctuations according to the way of approaching the quantum critical point. The results are in remarkable agreement with experiments for a wide variety of compounds exhibiting a quantum phase transition, as the ferroelectric oxides and other displacive systems.

Critical behaviour of thin films with quenched impurities.

The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method to the one-loop order within the framework of the n-component φ4-model. The finite-size crossover in impure films has been considered on the basis of the fundamental relationship between the effective dimensionality Deff and the characteristic lengths of the system. The fixed points, their stability properties and the critical exponents are obtained and analyzed, using an e=(4−Deff)-expansion near the effective spatial dimensionality Deff of the fluctuation modes in D-dimensional hyperslabs with two types of quenched impurities: point-like impurities with short-range random correlations and extended (linear) impurities with infinite-range random correlations along the small-size spatial direction. The difference between the critical properties of infinite systems and films is demonstrated and investigated. A new critical exponent, describing the scaling properties of the thickness of films with extended impurities has been derived and calculated. A special attention is paid to the critical behaviour of real impure films (D=3).

Dynamical critical exponent for quantum systems with long-range correlated impurities

Abstract The dynamical critical exponent of some quantum systems in the presence of long-range-correlated disorder is calculated with the use of a double renormalization group expansion. The impurity effects on the static critical behaviour in the quantum regime are also outlined.

Field-induced quantum criticality of systems with ferromagnetically coupled structural spin units

The field-induced quantum criticality of compounds with ferromagnetically coupled structural spin units (as dimers and ladders) is explored by applying Wilsons renormalization group framework to an appropriate effective action. We determine the low-temperature phase boundary and the behavior of relevant quantities decreasing the temperature with the applied magnetic field fixed at its quantum critical point value. In this context, a plausible interpretation of some recent experimental results is also suggested.

Random field effects in a Bose system: Critical behaviour and crossover phenomena in the Hartree limit

The low temperature grand canonical critical properties of a d-dimensional n-vector Bose system in the presence of a random field, which behaves like [h∗khk]av ∽ kθ (θ ⩾ 0), are investigated with the use of replica trick and the Hartree approximation. With a boson free particle spectrum, which behaves like kσ (0 < σ ⩽ 2), several situations occur, both at zero and non-zero temperature regimes, which are studied in detail for different values of d, σ, θ. In particular, some questions concerning the effective lowering of the space dimensionality and the violation of the usual scaling laws when the random field is present are also checked. Furthermore crossover phenomena appear where, alternatively, the random field intensity and the temperature assume the role of crossover parameter. It is shown that these crossover processes can be described in terms of crossover scaling functions and effective critical exponents in conformity with the standard crossover theory.

Erratum: Unified static renormalization-group treatment of finite-temperature crossovers close to a quantum critical point [Phys. Rev. B75, 014105 (2007)]

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.

Replica-symmetry breaking and quantum fluctuation effects in the p-spin interaction spin-glass model with a transverse field

The Ising infinite-range spin-glass model with p-spin interactions in the presence of a transverse field is studied for large but finite p using the Matsubara time representation and Parisis scheme of replica-symmetry breaking. In the spin-glass phase, the corrections to the limit appear much more essential than in the classical counterpart. It is shown that the quantum fluctuations have the effect of destroying the spin-glass order and a lower temperature is required to stabilize the spin-glass phase. The spin autocorrelation function in the spin-glass phase is explicitly calculated as a function of p and the Matsubara time. The result is just complementary and consistent with that previously obtained for the paramagnetic state without using the replica method.

Two-spin cluster approach to the infinite-range quantum transverse XY spin-glass model

Abstract The infinite-range quantum XY spin-glass model in the presence of a transverse field is considered and its phase diagram is determined using the two-spin cluster expansion method. It is shown that a spin-glass phase transition is possible for non-zero transverse field up to a zero-temperature value which equals twice the largest eigenvalue of the random bond interaction matrix.