On the Short Distance Behavior of the Critical Ising Model Perturbed by a Magnetic Field

We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with O.P.E. Wilson coefficients instead of correlators, all order I.R. safe formulas can be obtained for the perturbative expansion with respect to magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, that are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform have been used to compute the I.R. behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the Vacuum Expectation Value of the energy operator, left unfixed by usual nonperturbative approaches (Thermodynamic Bethe Ansatz).Comment: 19 pages, LATEX, 2 figure

Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators

We propose a general method for the numerical evaluation of OPE coefficients in three dimensional Conformal Field Theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising Model, looking at the magnetic perturbation of the , $<\sigma (\mathbf {r})\epsilon(0)>$ and correlators from which we extract the values of $C^{\sigma}_{\sigma\epsilon}=1.07(3)$ and $C^{\epsilon}_{\epsilon\epsilon}=1.45(30)$. Our estimate for $C^{\sigma}_{\sigma\epsilon}$ agrees with those recently obtained using conformal bootstrap methods, while $C^{\epsilon}_{\epsilon\epsilon}$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.Comment: 4 pages, typos corrected, a few references adde

Signatures of fractional Hall quasiparticles in moments of current through an antidot

The statistics of tunneling current in a fractional quantum Hall sample with an antidot is studied in the chiral Luttinger liquid picture of edge states. A comparison between Fano factor and skewness is proposed in order to clearly distinguish the charge of the carriers in both the thermal and the shot limit. In addition, we address effects on current moments of non-universal exponents in single-quasiparticle propagators. Positive correlations, result of propagators behaviour, are obtained in the shot noise limit of the Fano factor, and possible experimental consequences are outlined

Finite frequency noise for edge states at filling factor ν=2/5\nu=2/5

We investigate the properties of the finite frequency noise in a quantum point contact geometry for the fractional quantum Hall state at filling factor $\nu=2/5$. The results are obtained in the framework of the Wen's hierarchical model. We show that the peak structure of the colored noise allows to discriminate among different possible excitations involved in the tunneling. In particular, optimal values of voltage and temperature are found in order to enhance the visibility of the peak associated with the tunneling of a 2-agglomerate, namely an excitation with charge double of the fundamental one associated to the single quasiparticle.Comment: 5 pages, 1 figure, to be published in the Proceedings of the Conference on the Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT11

On the c-theorem in more than two dimensions

Several pieces of evidence have been recently brought up in favour of the c-theorem in four and higher dimensions, but a solid proof is still lacking. We present two basic results which could be useful for this search: i) the values of the putative c-number for free field theories in any even dimension, which illustrate some properties of this number; ii) the general form of three-point function of the stress tensor in four dimensions, which shows some physical consequences of the c-number and of the other trace-anomaly numbers.Comment: Latex, 7 pages, 1 tabl

Anomalous charge tunneling in the fractional quantum Hall edge states at filling factor \nu = 5/2

We explain effective charge anomalies recently observed for fractional quantum Hall edge states at $\nu=5/2$ [M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Phys.Rev. B. \textbf{81}, 161303(R) (2010)]. The experimental data of differential conductance and excess noise are fitted, using the anti-Pfaffian model, by properly take into account renormalizations of the Luttinger parameters induced by the coupling of the system with an intrinsic $1/f$ noise. We demonstrate that a peculiar agglomerate excitation with charge $e/2$, double of the expected $e/4$ charge, dominates the transport properties at low energies.Comment: 5 pages, 2 figure

On the Eigenfunction Expansions Associated with Fredholm Integral Equations of First Kind in the Presence of Noise

In this paper we consider the eigenfunction expansions associated with Fredholm integral equations of first kind when the data are perturbed by noise. We prove that these expansions are asymptotically convergent, in the sense of L 2 -norm, when the bound of the noise tends to zero. This result allows us to construct a continuous mapping from the data space to the solution space, without using any constraint or a priori bound. We can also show a probabilistic version of this result, which is based on the order)disorder transition in the Fourier coefficients of the noisy data. From these results one can derive algorithms and in particular statisti- cal methods able to furnish approximations of the solution without any use of prior knowledge. Q 1996 Academic Press, Inc

Fermions, Anomaly and Unitarity in High-Energy Electroweak Scattering

We report the "state of the art" of the problem of $B+L$ violation in high-energy electroweak scatterings. Results of various analyses point toward (though do not prove rigorously yet) the "half-suppression", i.e., that the $B+L$ violating cross section remains suppressed at least by the negative exponent of the single instanton action, at all energies. Most interesting techniques developed in this field are reviewed. Particular attention is paid to unitarity constraints on the anomalous cross section, and to some conceptual problem involving the use of the optical theorem in the presence of instantons.Comment: 59 (Latex) pages (+13 postscript figures (1075 blocks) available by e-mail request), GEF-Th-17/199

Study of the flux tube thickness in 3d LGT's by means of 2d spin models

We study the flux tube thickness in the confining phase of the (2+1)d SU(2) Lattice Gauge Theory near the deconfining phase transition. Following the Svetitsky-Yaffe conjecture, we map the problem to the study of the correlation function in the two-dimensional spin model with Z_2 global symmetry, (i.e. the 2d Ising model) in the high-temperature phase. Using the form factor approach we obtain an explicit expression for this function and from it we infer the behaviour of the flux density of the original (2+1)d LGT. Remarkably enough the result we obtain for the flux tube thickness agrees (a part from an overall normalization) with the effective string prediction for the same quantity