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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 63 (1988), S. 4001-4001 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We present the results of rigorous calculations for the ±J Ising spin-glass model on the Bethe lattice. The phase diagram for varying temperature and fraction of ferromagnetic bonds is derived near the paramagnetic phase boundary. In addition to the spin-glass and paramagnetic phases, we find a nontrivial ferromagnetic phase and a magnetized spin-glass phase, characterized by diverging Edwards–Anderson susceptibility. The recursion relation for the distribution of single-site magnetizations is studied as a dynamical system on an appropriate function space, the bulk thermodynamics is described by the attractors of the recursion relation, and the phase transitions correspond to bifurcations in the dynamics. Using bifurcation theory, we establish the existence of a stable distribution of single-site magnetizations near the paramagnetic phase boundary. At least in single-site properties, the existence proof precludes chaos, and infinite hierarchy of transitions, and other conceivable bizarre possibilities. While our phase diagram is very similar to the phase diagram for the Sherrington–Kirkpatrick model, the Bethe lattice provides a useful description of the mean-field behavior of spin glasses because the interactions are short range, the analysis is much more straightforward, and the results have been made completely rigorous.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 8816-8842 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: New features are resolved within the internal vibrational mode spectra of NO−2 defects in KCl, KBr, and KI crystals at low temperatures using high-resolution Fourier transform spectroscopy and persistent infrared spectral hole (PIRSH) burning separately and together. With interferometry it has been discovered that the vibrational linewidths of the different modes range over a factor of 300—from 0.01 cm−1 to ∼3 cm−1 and, with PIRSH burning, it has been demonstrated that the narrowest lines are inhomogeneously broadened while the broadest ones are homogeneously broadened. PIRSH's have been found in some internal modes and combination bands of the NO−2 molecule when pumped with low-intensity single-mode lead salt diode lasers; however, detectable persistent holes are not produced in all of the modes because of a competition between hole production and relaxation by tunneling at low temperatures. This competition results in a hole burning intensity, below which hole relaxation overwhelms hole production and only small holes may be produced.The most unusually shaped absorption features are the V-shaped notches in the reorientational tunneling fine structure at the NO−2 bending mode frequency in KCl and KBr. Of all the internal modes that do show pronounced PIRSH burning, these V-notched absorption bands exhibit the most striking behavior. Multiple satellite PIRSH's are detected at frequencies away from the single-mode laser burn frequency with a broadband probe beam produced by a high-resolution Fourier transform interferometer. An explanation for these satellite holes is derived from temperature, plastic deformation, and uniaxial stress dependence measurements on the KCl@B:NO−2 absorption spectrum. We find that the inhomogeneous broadening of the KCl@B:NO−2 ν2 reorientational tunneling fine structure is dominated by degenerate rotor level splitting produced by random crystal strains. Degenerate perturbation theory of the rotor level splitting in the strain field is found to match very closely the V-shaped inhomogeneous distribution of levels associated with the KCl@B:NO−2 reorientational tunneling fine structure. The general conclusion is that whenever strain splitting of a doubly degenerate level dominates the inhomogeneous broadening, then the absorption spectrum displays zero strength in the distribution at zero splitting and a linear increase in absorption coefficient away from this frequency generating the observed V-shaped notch in the absorption profile.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1572-9613
    Keywords: Spin glass ; Bethe lattice ; bifurcation ; critical phenomena
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a rigorous analysis of the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize the bulk ordered phases using bifurcation theory: we prove the existence of a distribution of single-site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1572-9613
    Keywords: Spin glass ; Bethe lattice ; multicritical point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this and the companion paper, we analyze the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize magnetized spin-glass (MSG) phases by divergence of an appropriate susceptibility: at zero field this signals the existence of an intermediate MSG phase; at nonzero field, this is used to identify the de Almeida-Thouless line.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of nonlinear science 6 (1996), S. 499-506 
    ISSN: 1432-1467
    Keywords: normal forms ; bifurcations ; Duffing equation ; Poincaré section ; Lie transform ; nonlinear Stokes phenomena ; 58F14 ; 58F36 ; 58F37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences of relaxing the restrictions of the form of the coordinate transformations. In the Duffing equation, a logarithmic transformation can remove the nonlinearity: in one interpretation, the nonlinearity is replaced by a branch cut leading to a Poincaré section. When the linearized problem is autonomous with diagonal Jordan form, we can remove all nonlinearities order by order using these singular coordinate transformations.
    Type of Medium: Electronic Resource
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