An analytical approach of the ergodic—non-ergodic transition in correlated systems
| Autor: | J. Souletie |
|---|---|
| Rok vydání: | 1994 |
| Předmět: |
Physics
Phase transition Condensed matter physics Ergodic hypothesis Condensed Matter Physics Plateau (mathematics) Power law Electronic Optical and Magnetic Materials symbols.namesake Quantum mechanics Materials Chemistry Ceramics and Composites Exponent Gaussian function symbols Relaxation (physics) Constant (mathematics) |
| Zdroj: | Journal of Non-Crystalline Solids. :108-112 |
| ISSN: | 0022-3093 |
| DOI: | 10.1016/0022-3093(94)90423-5 |
| Popis: | When a hierarchical criterion is associated with the renormalization of distances which governs the static properties near a phase transition, a non-exponential relaxation is found which is controlled by two timescales. The time constant, τβ, which controls the initial decays corresponds to local rearrangements and obeys thermal activation. The constant, τα, which controls the final approach to equilibrium corresponds to extended correlations and diverges at Tc where the system becomes non-ergodic. One finds τ β τ 0 ∼ ( ξ ξ 0 ) z ∼ [1 − ( T c T )] −zv . While P(1nτβ) is fixed by the nature of the local order, the distribution P(1nτα) which is the result of a cascade of renormalizations tends to become a gaussian of width λ, such that λ 2 − λ 0 2 ∝ 1 n ( τ α τ 0 ) . As a result, it is found that the out of phase susceptibility has a β-peak and an α-peak. The former shows a plateau followed by a power law those exponent is prooortional to T. The latter is essentially a Gaussian function of the 1n t variable with some skewness which can be represented by an error function. |
| Databáze: | OpenAIRE |
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