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Hierarchical solution and the structure of order parameters in the mean-field theory of spin glasses and related materials
Klíč, Antonín ; Janiš, Václav (advisor) ; Zahradník, Miloš (referee) ; Zdeborová, Lenka (referee)
We analyze the replica-symmetry-breaking (RSB) construction in the Sherrington - Kirkpatrick (SK) model and in the p-state Potts glass for p ≤ 4. We present a general scheme for deriving an asymptotic solution with an arbitrary number of discrete hierarchies of broken replica symmetry near the critical temperature for both models, and close to the de Almeida- Thouless instability line in the SK model. We show that in the SK model all solutions with finite many hierarchies are unstable and only the scheme with infinite many hierarchies becomes marginally stable in the spin-glass phase. For the Potts glass, we find, moreover, an one-step RSB solution which co- exists with the infinite RSB solution for p > p∗ ≈ 2.82. The former solution is locally stable but has lower free energy than the latter which is marginally stable and has the highest free energy. 1
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The development of magnetic behavior in the PrNi1-xCuxAl compounds
Fikáček, Jan
Title: The development of magnetic behavior in the PrNi1-xCuxAl compounds Author: Bc. Jan Fikáček Department: Department of Condensed Matter Physics Supervisor: Doc. Mgr. Pavel Javorský, Dr. Supervisor's e-mail address: javor@mag.mff.cuni.cz Abstract: In the present work we studied magnetic properties of the substituted PrNi1-xCuxAl series. A very interesting behavior had been reported in the previously studied systems with the same substitution, but with different rare earths contained, e.g. loss of long range order for certain concentrations of copper. We prepared polycrystalline samples of the PrNi1-xCuxAl (x = 0.1 - 0.9, 9 different stoichiometries) and measured them using X-ray diffraction, specific heat, magnetization and AC susceptibility. Additionally, powder neutron diffraction measurement on PrNi0.2Cu0.8Al sample was performed in ILL (Institut Laue Langevin) in Grenoble. Results of measurements on these compounds show on the presence of a long order in case of compounds with x = 0.1 - 0.4 below the ordering temperatures in the range of 3.4 - 5 K. Measurements of AC susceptibility and neutron diffraction revealed the loss of long range order in the rest of the series. In these compounds, the development of a spin glass state occurs below the temperatures between 3.4 and 4.5 K.
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Hierarchical solution and the structure of order parameters in the mean-field theory of spin glasses and related materials
Klíč, Antonín ; Janiš, Václav (advisor) ; Zahradník, Miloš (referee) ; Zdeborová, Lenka (referee)
We analyze the replica-symmetry-breaking (RSB) construction in the Sherrington - Kirkpatrick (SK) model and in the p-state Potts glass for p ≤ 4. We present a general scheme for deriving an asymptotic solution with an arbitrary number of discrete hierarchies of broken replica symmetry near the critical temperature for both models, and close to the de Almeida- Thouless instability line in the SK model. We show that in the SK model all solutions with finite many hierarchies are unstable and only the scheme with infinite many hierarchies becomes marginally stable in the spin-glass phase. For the Potts glass, we find, moreover, an one-step RSB solution which co- exists with the infinite RSB solution for p > p∗ ≈ 2.82. The former solution is locally stable but has lower free energy than the latter which is marginally stable and has the highest free energy. 1
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The development of magnetic behavior in the PrNi1-xCuxAl compounds
Fikáček, Jan
Title: The development of magnetic behavior in the PrNi1-xCuxAl compounds Author: Bc. Jan Fikáček Department: Department of Condensed Matter Physics Supervisor: Doc. Mgr. Pavel Javorský, Dr. Supervisor's e-mail address: javor@mag.mff.cuni.cz Abstract: In the present work we studied magnetic properties of the substituted PrNi1-xCuxAl series. A very interesting behavior had been reported in the previously studied systems with the same substitution, but with different rare earths contained, e.g. loss of long range order for certain concentrations of copper. We prepared polycrystalline samples of the PrNi1-xCuxAl (x = 0.1 - 0.9, 9 different stoichiometries) and measured them using X-ray diffraction, specific heat, magnetization and AC susceptibility. Additionally, powder neutron diffraction measurement on PrNi0.2Cu0.8Al sample was performed in ILL (Institut Laue Langevin) in Grenoble. Results of measurements on these compounds show on the presence of a long order in case of compounds with x = 0.1 - 0.4 below the ordering temperatures in the range of 3.4 - 5 K. Measurements of AC susceptibility and neutron diffraction revealed the loss of long range order in the rest of the series. In these compounds, the development of a spin glass state occurs below the temperatures between 3.4 and 4.5 K.
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