Asymptotic Description of Schematic Models for CKN

TL;DR

This paper analyzes schematic models for CKN using asymptotic expansions, validating the power-law and Cole-Cole-peak solutions, and explaining deviations in observed exponents through correction terms.

Contribution

It provides an asymptotic analysis of schematic models for CKN, demonstrating the validity of different spectral expansions and explaining observed deviations in critical exponents.

Findings

Both expansions fit the data well up to next-to-leading order.

Effective power-law exponents are about 15% smaller than theoretical values.

Crossover to alpha-peak spectrum causes smaller exponents at higher temperatures.

Abstract

The fits of 0.4 Ca(NO_3)_2 0.6 K(NO_3) (CKN) by schematic mode-coupling models [V. Krakoviack and C. Alba-Simionesco, J. Chem. Phys. 117, 2161-2171 (2002)] are analyzed by asymptotic expansions. The validity of both the power-law and the Cole-Cole-peak solutions for the critical spectrum are investigated. It is found that the critical spectrum derived from the fits is described by both expansions equally well when both expansions are carried out up to next-to-leading order. The expansions up to this order describe the data for 373K over two orders of magnitude in frequency. In this regime an effective power law omega^a can be identified where the observed exponent $a$ is smaller than its calculated value by about 15%; this finding can be explained by corrections to the leading-order terms in the asymptotic expansions. For higher temperatures, even smaller effective exponents are caused by a crossover to the alpha-peak spectrum.