14,617 research outputs found
Simultaneous observation of small- and large-energy-transfer electron-electron scattering in three dimensional indium oxide thick films
In three dimensional (3D) disordered metals, the electron-phonon
(\emph{e}-ph) scattering is the sole significant inelastic process. Thus the
theoretical predication concerning the electron-electron (\emph{e}-\emph{e})
scattering rate as a function of temperature in 3D
disordered metal has not been fully tested thus far, though it was proposed 40
years ago [A. Schmid, Z. Phys. \textbf{271}, 251 (1974)]. We report here the
simultaneous observation of small- and large-energy-transfer \emph{e}-\emph{e}
scattering in 3D indium oxide thick films. In temperature region of
\,K, the temperature dependence of resistivities curves of the
films obey Bloch-Gr\"{u}neisen law, indicating the films possess degenerate
semiconductor characteristics in electrical transport property. In the low
temperature regime, as a function of for each film can not
be ascribed to \emph{e}-ph scattering. To quantitatively describe the
temperature behavior of , both the 3D small- and
large-energy-transfer \emph{e}-\emph{e} scattering processes should be
considered (The small- and large-energy-transfer \emph{e}-\emph{e} scattering
rates are proportional to and , respectively). In addition, the
experimental prefactors of and are proportional to
and ( is the Fermi wave number,
is the electron elastic mean free path, and is the Fermi energy),
respectively, which are completely consistent with the theoretical
predications. Our experimental results fully demonstrate the validity of
theoretical predications concerning both small- and large-energy-transfer
\emph{e}-\emph{e} scattering rates.Comment: 5 pages and 4 figure
The tensor renormalization group study of the general spin-S Blume-Capel model
We focus on the special situation of of the general spin-S Blume-Capel
model on the square lattice. Under the infinitesimal external magnetic field,
the phase transition behaviors due to the thermal fluctuations are discussed by
the newly developed tensor renormalization group method. For the case of the
integer spin-S, the system will undergo first-order phase transitions with
the successive symmetry breaking with the magnetization . For the
half-integer spin-S, there are similar first order phase transition
with stepwise structure, in addition, there is a continuous
phase transition due to the spin-flip symmetry breaking. In the low
temperature regions, all first-order phase transitions are accompanied by the
successive disappearance of the optional spin-component pairs(),
furthermore, the critical temperature for the nth first-order phase transition
is the same, independent of the value of the spin-S. In the absence of the
magnetic field, the visualization parameter characterizing the intrinsic
degeneracy of the different phases clearly demonstrates the phase transition
process.Comment: 6 pages, 7 figure
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