Lower and upper bounds on the fidelity susceptibility

We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, like susceptibilities and thermal average values. The quality of the bounds is checked by the exact expressions for a single spin in an external magnetic field. Their usefulness is illustrated by two examples of many-particle models which are exactly solved in the thermodynamic limit: the Dicke superradiance model and the single impurity Kondo model. It is shown that as far as divergent behavior is considered, the fidelity susceptibility and the thermodynamic susceptibility are equivalent for a large class of models exhibiting critical behavior.Comment: 19 page

On the Finite-Temperature Generalization of the C-theorem and the Interplay between Classical and Quantum Fluctuations

The behavior of the finite-temperature C-function, defined by Neto and Fradkin [Nucl. Phys. B {\bf 400}, 525 (1993)], is analyzed within a d -dimensional exactly solvable lattice model, recently proposed by Vojta [Phys. Rev. B {\bf 53}, 710 (1996)], which is of the same universality class as the quantum nonlinear O(n) sigma model in the limit $n\to \infty$. The scaling functions of C for the cases d=1 (absence of long-range order), d=2 (existence of a quantum critical point), d=4 (existence of a line of finite temperature critical points that ends up with a quantum critical point) are derived and analyzed. The locations of regions where C is monotonically increasing (which depend significantly on d) are exactly determined. The results are interpreted within the finite-size scaling theory that has to be modified for d=4. PACS number(s): 05.20.-y, 05.50.+q, 75.10.Hk, 75.10.Jm, 63.70.+h, 05.30-d, 02.30Comment: 15 pages LATEX, ioplppt.sty file used, 6 EPS figures. Some changes made in section V (on finite-size scaling interpretation of the results obtained

Population of isomers in decay of the giant dipole resonance

The value of an isomeric ratio (IR) in N=81 isotones ($^{137}$Ba, $^{139}$Ce, $^{141}$Nd and $^{143}$Sm) is studied by means of the ($\gamma, n)$ reaction. This quantity measures a probability to populate the isomeric state in respect to the ground state population. In ($\gamma, n)$ reactions, the giant dipole resonance (GDR) is excited and after its decay by a neutron emission, the nucleus has an excitation energy of a few MeV. The forthcoming $\gamma$ decay by direct or cascade transitions deexcites the nucleus into an isomeric or ground state. It has been observed experimentally that the IR for $^{137}$Ba and $^{139}$Ce equals about 0.13 while in two heavier isotones it is even less than half the size. To explain this effect, the structure of the excited states in the energy region up to 6.5 MeV has been calculated within the Quasiparticle Phonon Model. Many states are found connected to the ground and isomeric states by $E1$, $E2$ and $M1$ transitions. The single-particle component of the wave function is responsible for the large values of the transitions. The calculated value of the isomeric ratio is in very good agreement with the experimental data for all isotones. A slightly different value of maximum energy with which the nuclei rest after neutron decay of the GDR is responsible for the reported effect of the A-dependence of the IR.Comment: 16 pages, 4 Fig

On the Finite Size Scaling in Disordered Systems

The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension $d=4-\epsilon$ and some universal results are obtained. The problem of self-averaging is clarified for different critical regimes.Comment: 21 pages, 2 figures, submitted to the Physcal Review

Theory of a spherical quantum rotors model: low--temperature regime and finite-size scaling

The quantum rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general geometry of the form $L^{d-d'}\times\infty^{d'}\times L_{\tau}^{z}$ ( $L$-linear space size and $L_{\tau}$-temporal size) and subjected to periodic boundary conditions. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0\leq d'\leq d$ a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.Comment: 33pages, revtex+epsf, 3ps figures included submitted to PR

First-Order Phase Transition with Breaking of Lattice Rotation Symmetry in Continuous-Spin Model on Triangular Lattice

Using a Monte Carlo method, we study the finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with or without easy-plane anisotropy. The model takes account of competing interactions: a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third nearest-neighbor interaction $J_3$. As a result, the ground state is a spiral spin configuration for $-4 < J_1/J_3 < 0$. In this structure, global spin rotation cannot compensate for the effect of 120-degree lattice rotation, in contrast to the conventional 120-degree structure of the nearest-neighbor interaction model. We find that this model exhibits a first-order phase transition with breaking of the lattice rotation symmetry at a finite temperature. The transition is characterized as a $Z_2$ vortex dissociation in the isotropic case, whereas it can be viewed as a $Z$ vortex dissociation in the anisotropic case. Remarkably, the latter is continuously connected to the former as the magnitude of anisotropy decreases, in contrast to the recent work by Misawa and Motome [J. Phys. Soc. Jpn. \textbf{79} (2010) 073001.] in which both the transitions were found to be continuous.Comment: 11pages, 16figures, accepted to JPS

Leydig cell-immune cell interaction: an example of neuroendocrine-immune communication in testis

In her paper "Tilings will never be the same again" Dr Kathleen L. Wishner quoted Alvin Toffler's book Future Shock written in 1970. Toffler defined "future shock" as a time phenomenon, a product of the greatly accelerated change in society. The scientific research itself is a demonstration of this accelerated change. In particular, data systematized by Davidoff et al in this volume of Biomedical Reviews indicate the change in the understanding of the nature and origin of Leydig cells of the human testis.Biomedical Reviews 1996; 6: 1-4

A suggestive neurotrophic potential of mast cells in heart and submandibular glands of the rat

According to the neurotrophic theory, the nerve growth factor (NGF) is widely distributed in the effector tissues of peripheral sympathetic and sensory neurons, suggesting that the density of innervation is controlled by effector derived NGF. Sympathetic neurons require access to NGF for survival throughout life, whereas sensory neurons are dependent on NGF only during restricted period of embryonic development. This development-related feature of sympathetic neurons suggests that they crucially depend on plasticity of NGF biology, including secretion, availability, and utilization, to maintain appropriate neuronal function in adult life, and even in old age. While most previous studies on the cellular source of NGF have focused on neuronal and nonneuronal effector cells, it was recently demonstrated that NGF secretion is not only restricted to cells receiving a direct innervation. Immune cells, including mast cells (MC), lymphocytes and macrophages, for example, produce and release NGF as well as NGF secretion-inducing cytokines. Likewise, since the first evidence that NGF treatment causes a significant increase in the number and size of MC has been published by Aloe and Levi-Montalcini in 1977, it has been repeatedly shown that these cells are also NGF-responsive cells, thus providing further evidence for a widely investigated MC-nerve interaction. Further on this trophobiological line, a positive correlation of the amount of NGF and expression of NGF mRNA with the density of sympathetic innervation was demonstrated in a variety of organs. In the rat heart, one such example, the atrium contains a higher amount of NGF corresponding to a denser sympathetic nerve supply compared to the ventricle. Such a correlation was also revealed in the submandibular glands (SMG) and iris. Likewise, the density of MC in the ankle joint capsule, which is heavily innervated, is greater than in the capsule of the knee, which is less densely innervated, and the MC number in the synovial joint of spontaneously hypertensive rats, which have increased sympathetic nerve supply, is significantly greater than in normotensive rats. A summing-up of the above mentioned data shows that (i) MC are NGF secreting/responsive cells and frequently colocalized with nerves, and (ii) a higher NGF amount correlates with a denser sympathetic innervation of a tissue . This, in our eyes, brings into question the sole contribution of the "classical" effector cells to neurotrophic support of sympathetic nerve-innervated tissues. Consequently, we suggest that MC, through their own and/or cytokine-induced NGF secretion, may also be implicated in the neurotrophic potential in these tissues.Biomedical Reviews 1998; 9: 143-145