A. Caramico D'Auria

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.

The spectral-density approach to an antiferromagnetic Heisenberg linear chain

SummaryWe study an antiferromagnetic Heisenberg linear chain (AHLC) by using the spectral-density method (SDM). The values of the thermodynamic quantities are obtained as functions of the temperature; our results are compared with the exact ones obtained by other authors atT=0.RiassuntoSi studia una catena lineare antiferromagnetica di Heisenberg (AHLC) usando il metodo delle densità spettrali (SDM). Il metodo permette di ottenere i valori delle grandezze termodinamiche in funzione della temperatura; si paragonano i risultati ottenuti con quelli esatti ottenuti da altri autori aT=0.РезюмеМы исследуем антиферромагнитные линейные цепочки Гайзенберга, используя метод спектральной плотности. Получаются значения термодинамических величин, как функции температуры. Наши результаты сравниваются с точными значениями, полученными другими авторами приT=0.

Spectral density method in classical statistical mechanics

Abstract The spectral density method in classical statistical mechanics is formulated and application to a linear classical spin system is made in the simplest approximation.

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.

Exact simulations of quantum rings and characterization of hexanuclear manganese and dodecanuclear nickel cyclic complexes

A numerical transfer-matrix approach and diagonalization technique exploiting the point-group symmetry are worked out in the framework of quantum statistical mechanics and group theory as exact simulation tools for application to thermodynamical properties of finite rings. They are applied to the isotropic spin models of the high-nuclearity cyclic clusters [Mn(hfac)2NITPh]6 and Ni12(O2CMe)12(chp)12(H2O)6(THF)6. The microscopic parameters of both molecules (J/kB = 350?10?K and J/kB = 8.5?0.5?K, respectively, with g = 2.23?0.01) are then obtained from a fit of the theoretical susceptibility curves to the experimental results.

Static properties of quantum spin S=1 chains: TMNB, TMNC and CsNiF3

The zero-field parallel and perpendicular susceptibility and the zero-field specific heat of the quantum easy-plane S=1 Heisenberg spin chains are calculated numerically and applied to TMNB, TMNC and CsNiF3. New values of the model parameters are estimated from fitting procedures. As to CsNiF3, the in-plane specific heat, the field-dependent magnetization and the spin-wave dispersion are also evaluated for a given choice of the microscopic parameters (J/kB=20.5 K, A/J=0.425) and compared with measured quantities. An overall agreement with experiment is revealed.

A proposal to include damping effects in the spectral density approach

Recently there has been proposed a modification of the spectral density method (SDM) to take into account damping effects for Fermi systems. There are in any case some difficulties concerning Bose and classical systems. The authors suggest a simple way of avoiding such difficulties and preserving the earliest idea for discussing damping effects. A classical ferromagnetic linear chain in external magnetic field is studied.

Spectral density approach for the damping of fermion elementary excitations in an anisotropic spin-12 linear chain

The paper is devoted to an investigation of the damping effects of the Fermion elementary excitations in the Jordan-Wigner representation of a one-dimensional anisotropic spin-12 model in an external field. This is realized on the basis of the “Gaussian ansatz”, recently proposed by Nolting and Oles, as substituting the standard “polar ansatz” in the Spectral Density Method, for exploring damping effects of quasi-particles in many-body problems. By using a first order approximation, we are able to obtain reasonable results in the low temperature limit.

Low-temperature behaviour of the transverse Ising model in the influence domain of the quantum critical point

Abstract The critical properties of the d -dimensional transverse Ising model in the influence domain of its quantum critical point are studied solving the one-loop renormalization group equations around and at d =3. Different critical regimes occur involving crossover behaviours which can be described in terms of effective exponents, consistently with the conventional crossover theory.