Non-power-law tail of structure factor in the large-n O(n) model

1999 ◽  
Author(s):  
Hiroyasu Toyoki
Keyword(s):  
2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Lisa Markhof ◽  
Mikhail Pletyukov ◽  
Volker Meden

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and used to compute the single-particle spectral function. This forms the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order perturbative contribution to the structure factor was so far not studied. We first close this gap and show that it is consistent with the conjectured power law. Secondly, we critically assess the steps leading to the mobile impurity Hamiltonian. We show that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This dependence was recently shown to spoil power laws in the single-particle spectral function which previously were believed to be part of the Tomonaga-Luttinger liquid universality. Although our second order results for the structure factor are consistent with power-law scaling, this raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal. We conclude that more work is required to clarify this.


2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
E. M. Anitas

Using the small-angle scattering method, we calculate here the mono- and polydisperse structure factor from an idealized fragmentation model based on the concept of renormalization. The system consists of a large number of fractal microobjects which are randomly oriented and whose positions are uncorrelated. It is shown that, in the fractal region, the monodisperse form factor is characterized by a generalized power-law decay (i.e., a succession of maxima and minima superimposed on a simple power-law decay) and whose scattering exponent coincides with the fractal dimension of the scatterer. The present analysis of the scattering structure factor allows us to obtain the number of fragments resulted at a given iteration. The results could be used to obtain additional structural information about systems obtained through microscale fragmentation processes.


2018 ◽  
Vol 115 (20) ◽  
pp. 5140-5144 ◽  
Author(s):  
Ilia Khait ◽  
Patrick Azaria ◽  
Claudius Hubig ◽  
Ulrich Schollwöck ◽  
Assa Auerbach

The doped 1D Kondo Lattice describes complex competition between itinerant and magnetic ordering. The numerically computed wave vector-dependent charge and spin susceptibilities give insights into its low-energy properties. Similar to the prediction of the large N approximation, gapless spin and charge modes appear at the large Fermi wave vector. The highly suppressed spin velocity is a manifestation of “heavy” Luttinger liquid quasiparticles. A low-energy hybridization gap is detected at the small (conduction band) Fermi wave vector. In contrast to the exponential suppression of the Fermi velocity in the large-N approximation, we fit the spin velocity by a density-dependent power law of the Kondo coupling. The differences between the large-N theory and our numerical results are associated with the emergent magnetic Ruderman–Kittel–Kasuya–Yosida interactions.


1991 ◽  
Vol 248 ◽  
Author(s):  
K. Svoboda ◽  
C.F. Schmidt ◽  
N. Lei ◽  
C.R. Safinya ◽  
S.M. Block ◽  
...  

AbstractWe studied the conformation of the membrane skeleton of human red blood cells (RBC) after detergent extraction of RBC ghosts, using video microscopy, light scattering, and synchrotronbased small angle X-ray scattering (SAXS). RBC membrane skeletons are two-dimensionally connected, triangulated networks of flexible, polyionic proteins. Immediately after extraction, the skeletons exhibited large-scale thermal undulations and deformed strongly in weak shear flow. Screening of electrostatic repulsion by immersion in high ionic strength buffer led to shrinkage, while the shell-like conformations and the flexibility of the skeletons were preserved. Under high ionic strength conditions (1 M monovalent salt), the static structure factor, S(q), showed two power law regimes S(q) ∝ q −α, with α <≈ 2.0 in the range of wave vectors 4×10−4 Å−1 < g < 8×10−4 Å−1, and α = 2.3 ± 0.1 in the range of wave vectors 8×10−4 Å−1 < q < l×10−1 Å−1. The same power law behavior was observed in low ionic strength buffer (25 mM salt) for q < 2×10−3 Å−1. This result is not consistent with the occurence of a crumpling transition during skeleton shrinkage. The observed form of the static structure factor, with a transition between two regimes with different power law exponents, presents evidence for the theoretically predicted flat phase of 2D-polymers.


2018 ◽  
Vol 33 (38) ◽  
pp. 1850223 ◽  
Author(s):  
Miloslav Znojil ◽  
Iveta Semorádová

Anharmonic oscillator is considered using an unusual, logarithmic form of the anharmonicity. The model is shown connected with the more conventional power-law anharmonicity [Formula: see text] in the limit [Formula: see text]. An efficient and user-friendly method of the solution of the model is found in the large-N expansion technique.


1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.


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