PACS. 75.10.Nr -Spin-glass and other random models. PACS. 84.35.+i -Neural networks.Abstract. -The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative approach leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results below the instability are presented and the consequences for the dynamical mean field equations are discussed.Introduction. -Together with the replica approach, the Thouless-Anderson-Palmer (TAP) approach [1] is the most important method to analyze infinite range spin glass models like the Sherrington-Kirkpatrick (SK) model [2] of Ising spins (for reviews see [3,4]). The TAP equations are well established [3][4][5] and are exact in the thermodynamic limit (N → ∞) provided that the local magnetizations {m i } satisfy the condition
For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in combination with a phenomenological relaxational dynamics used as a numerical tool. For all temperatures and all bond configurations stable and meta stable states are found. Following a discussion of the finite size effects, the static properties of the state of lowest free energy are presented in the presence of a homogeneous magnetic field for all temperatures below the spin glass temperature. Moreover some characteristic features of the meta stable states are presented. These states exist in finite temperature intervals and disappear via local saddle node bifurcations. Numerical evidence is found that the excess free energy of the meta stable states remains finite in the thermodynamic limit. This implies a the 'multi-valley' structure of the free energy on a sub-extensive scale.
The ESR spectra of Gd in metallic single crystals of LaSb exhibit appreciable variation in the ESR line shape upon changing the temperature from 1.7 to 300 K. At low temperatures, a completely resolved fine-structure splitting appropriate to Gd in a cubic crystalline field is observed. The fourth-order cubic-crystalline-field parameter is b4 --+ 32+ 2 Oe. The increase of the temperature leads to significant narrowing effects with the result of a single anisotropic line at room temperature. A Korringa relaxation rate of AH K/T = 0,19 + 0.03 Oe/K was extracted from the thermal broadening of the collaosed spectrum. The thermal broadening of the -1/2~+1/2 fine-structure transition is considerably enhanced, however, with respect to this Korringa thermal broadening. All these features are in complete agreement with the predictions of the theory for exchange narrowing of the fine structure in metals. The ESR line shape was calculated using this theory. Comparison of the theoretical line shape with the one observed experimentally indicates the presence of an additional narrowing mechanism, This narrowing is due to Gd spin-spin interaction in LaSb. The line shape analysis yields an exchange-interaction parameter of 0.03 eV between the spin of Gd and that of the conduction electron. The same value for the exchange parameter is derived, independently, from the experimental Korringa thermal broadening.
The influence of crystal fields on the dynamic transverse susceptibility of localized spin moments coupled to the conduction electrons in a metal is investigated. In Liouville-space, the projector onto the subspace is introduced which is spanned by the transverse component of the conduction electron magnetization and the transition operators of the crystal field energy levels. Within the framework of projector formalism, the susceptibility is expressed in terms of a transition matrix which is then calculated in lowest order perturbation theory. The found explicit expression of the susceptibility is valid for the isothermal case as well as for the bottleneck one. The theoretical predicted resolved and unresolved ESR spectra are discussed for high and low temperature. For the bottleneck and the isothermal case, a resolved spectrum is expected when crystal field splittings are greater than the Korringa relaxation rate.Es wird der EinfluB von Kristallfeldern auf die transversale dynamische Suszeptibilitat lokalisierter Spin-Momente untersucht, die an die Leitungselektronen in einem Metal1 angekoppelt sind. I m Liouville-Raum wird der Projektor auf den Unterraum eingefuhrt, der von der transversalen Komponente der Leitungselektronen-Magnetisierung und den tfbergangsoperatoren der Krist,allfeld-Energiezustande aufgespannt wird. Mit Hilfe des Projektorformalismus wird die Suszeptibilitat durch eine Ubergangsmatrix ausgedriickt, die dann in Storungstheorie niedrigster Ordnung bestimmt wird. Der gefundene explizite Ausdruck fur die Suszeptibilitat ist gultig sowohl fur den isothermen als auch den ,,bottleneck"-Fall. Die theoretisch vorhergesagten aufgelosten und unaufgelosten ESR Spektren werden fur hohe und tiefe Temperaturen diskutiert. Fur den ,,bottleneck" und den isothermen Fall wird ein aufgelostes Spektrum erwartet, falls die Kristallfeldaufspaltung groBer als die Korringa-R.elaxationsrate ist.
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