G. Busiello

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.

Renormalization group approach to quantum bosonized systems

SummaryTo leading order in a perturbative renormalization group analysis we study the critical behaviour of Bose and related quantum systems at temperatureT≠0 andT−0, for which a preliminary investigation has been reported recently. In both cases we specify the meaning of the grand canonical variable which corresponds to the usual critical deviationT−Tc in the canonical Wilson scheme. In particular, forT≠0, when the grand canonical critical exponents are the same as the classical one, we calculate the canonical critical exponents with the use of Fisher’s renormalization relations. The question of dimensional crossover which appears forT→0 is briefly discussed. For the more interesting caseT=0, the critical surface and the exponents associated with the stable nontrivial fixed point are calculated. We discover an unusual behaviour which, nevertheless, can be still included in a universality class in Wilson’s sense.RiassuntoAll’ordine dominante in un’analisi perturbativa del gruppo di rinormalizzazione si effettua uno studio di sistemi quantistici bosonici a temperaturaT≠0 eT−0, per cui è stata fornita recentemente un’indagine preliminare. In entrambi i casi si specifica il significato della variabile gran canonica corrispondente all’usuale deviazione criticaT−Tc nello schema canonico di Wilson. In particolare, nel casoT≠0, in cui gli esponenti critici gran canonici si identificano con quelli di un sistema classico, facendo uso delle relazioni di rinormalizzazione di Fisher, si calcolano gli esponenti critici canonici. Il problema dell’incrocio dimensionale che appare perT→0 è esaminato brevemente. Per il caso più interessanteT=0, si determinano la superficie critica e gli esponenti critici associati al punto fisso non banale stabile. Dai risultati emerge un comportamento insolito che, tuttavia, può essere incluso in una classe di universalità nel senso di Wilson.РезюмеВ главном порядке при пертурбационном анализе группы перенормировки мы исследуем критическое поведение квантовых Бозе-систем при температуреT≠0 иT=0. В обоих случаях мы определяем физический смысл главной канонической переменной, которая соответствует обычному критическому отклонениюT−Tc в канонической схеме Вильсона. В частности, дляT≠0, когда главные канонические критические показатели являются такими же, как для классических систем, мы вычисляем канонические критические показатели с использованием соотношений перенормировки Фишера. Вкратце обсуждается вопрос размерного кроссовера, который возникает дляT→0. Для наиболее интересного случаяT=0 вычисляются критические поверхности и показатели, связанные с устойчивой нетривиальной фиксированной точкой. Мы обнаружили необычное поведение, которое, тем не менее, может быть включено в универсальный класс в смысле Вильсона.

The critical exponents η and z to second order in ϵ=2−d for a Bose system at T=0

Abstract The critical exponents η and z for a d -dimensional Bose system at T =0 are calculated to second order in ϵ =2− d via Wilsons renormalization group approach. The result seems to confirm that a cross-over ( d , n =2)→( d +2, n =−2) occurs for T →0.

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.

Paleodiet characterisation of an Etrurian population of Pontecagnano (Italy) by Isotope Ratio Mass Spectrometry (IRMS) and Atomic Absorption Spectrometry (AAS)

Human bones recovered from the archaeological site of Pontecagnano (Salerno, Italy) have been studied to reconstruct the diet of an Etrurian population. Two different areas were investigated, named Library and Sant’ Antonio, with a total of 44 tombs containing human skeletal remains, ranging in age from the 8th to the 3rd century B.C. This time span was confirmed by 14C dating obtained using Accelerator Mass Spectrometry (AMS) on one bone sample from each site. Atomic Absorption Spectrometry (AAS) was used to extract information about the concentration of Sr, Zn, Ca elements in the bone inorganic fraction, whilst stable isotope ratio measurements (IRMS) were carried out on bone collagen to obtain the δ13C and δ15N. A reliable technique has been used to extract and separate the inorganic and organic fractions of the bone remains. Both IRMS and AAS results suggest a mixed diet including C3 plant food and herbivore animals, consistent with archaeological indications. #Revised version of a paper presented at the 1st Joint European Stable Isotope Users Group Meeting (JESIUM), August, 30 to September, 3, 2004, Vienna, Austria

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.

Thermodynamic properties of the low-dimensional perfect Bose gas

The chemical potential, the specific heat and the correlation function are obtained for the perfect Bose gas at a constant volume at low spatial dimensionalities. The Bose-Einstein condensation occurs only at zero temperature. Some nonuniversal features of this condensation are discussed.

Quenched impurities and tricriticality in classical and quantum systems

A generalised model, intended to describe a number of quantum systems in the presence of short-range correlated quenched impurities, is studied by the renormalisation group approach. To first order in epsilon , it is shown that the tricritical behaviour is unstable towards impurity perturbations for both finite and zero temperatures. A brief discussion of the zero-temperature tricriticality in pure systems is also presented.

Effect of magnetic fluctuations on the normal-state properties of Sr2RuO4

We investigate the normal-state transport properties of Sr2RuO4 and we show that a consistent explanation of the experimental results can be obtained assuming that the system is near a quantum phase transition. Within the framework of a self-consistent spin fluctuation theory, we calculate the temperature variation of some relevant physical quantities and we discuss a possible microscopic origin of the quantum phase transition.

Low-temperature orientational-glass-like phase transition in glass model

Abstract A simplified model of low-temperature orientational-glass-like phase transition from orientationally disordered phase to orientational glass phase in dielectric glass is presented. The model predicts a freezing of the defect orientations in random directions like the spin-glass phase in magnetic materials. A cusp of the orientational defect susceptibility is found. The second-order phase-transition temperature is defined by the strength of the interaction between the orientational degrees of freedom of the tunnelling defects in glass.