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.Comment: 36 pages, 2 figures, accepted in Physica

Quantum tricriticality in transverse Ising-like systems

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3<d<4, with a clear location of the critical lines ending in the conventional quantum critical points and in the quantum tricritical one, and of the tricritical line for temperature T \geq 0. We determine also the critical and the tricritical shift exponents close to the corresponding ground state instabilities. Remarkably, we find a tricritical shift exponent identical to that found in the conventional quantum criticality and, by approaching the quantum tricritical point increasing the non-thermal control parameter r, a crossover of the quantum critical shift exponents from the conventional value \phi = 1/(d-1) to the new one \phi = 1/2(d-1). Besides, the projection in the (r,T)-plane of the phase boundary ending in the quantum tricritical point and crossovers in the quantum tricritical region appear quite similar to those found close to an usual quantum critical point. Another feature of experimental interest is that the amplitude of the Wilsonian classical critical region around this peculiar critical line is sensibly smaller than that expected in the quantum critical scenario. This suggests that the quantum tricriticality is essentially governed by mean-field critical exponents, renormalized by the shift exponent \phi = 1/2(d-1) in the quantum tricritical region.Comment: 9 pages, 2 figures; to be published on EPJ

Classical transverse Ising spin glass with short- range interaction beyond the mean field approximation

The classical transverse field Ising spin- glass model with short-range interactions is investigated beyond the mean- field approximation for a real d- dimensional lattice. We use an appropriate nontrivial modification of the Bethe- Peierls method recently formulated for the Ising spin- glass. The zero- temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d. The phase diagram is also calculated numerically for different values of d. In the limit d -> infinity, known mean- field results are consistently reproduced.Comment: LaTex, 11 pages, 2 figure

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 Wilson's 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.Comment: to be published in Physics Letters

Dome-shaped phase diagram in the spin-1 XY ferromagnet with biquadratic exchange and longitudinal easy-axis crystal field

We investigate the phase diagram of a spin-1 ferromagnetic XY model in the presence of a longitudinal easy-axis crystal field assuming bilinear (J) and biquadratic (I) exchange interactions between nearest neighbors spins and using the two-time Green Functions framework at the level of the Devlin strategy. Employing both analytical estimates and numerical calculations, we find that the structure of the crystal-field-induced phase boundary changes sensibly as the ratio α=I/J increases. In particular, when α overcomes a characteristic value α*, two quantum critical points appear which are connected by a dome-shaped critical line. Due to the paradigmatic nature of the anisotropic spin model here considered, we believe that our findings may provide useful insights into the physical origin of recent experimental results found for some innovative materials which exhibit two quantum critical points and dome-shaped phase diagrams induced by non-thermal control parameters driving a non-conventional quantum criticality