Theory of Non-linear Susceptibility and Correlation Length in Glasses and Liquids

Claudio Donati; Silvio Franz; Giorgio Parisi; Sharon C. Glotzer

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Theory of Non-linear Susceptibility and Correlation Length in Glasses and Liquids

Claudio Donati·Silvio Franz·Giorgio Parisi·Sharon C. Glotzer

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Abstract

Within the framework of the effective potential theory of the structural glass transition, we calculate for the p-spin model a static nonlinear susceptibility related to a four-point density correlation function, and show that it grows and diverges in mean field with exponent $γ=1/2$ as the mode coupling critical temperature T_c is approached from below. When T_c is approached from above, we calculate within the mode coupling framework a dynamic nonlinear susceptibility and show that there is a characteristic time where the susceptibility is a maximum, and that this time grows with decreasing T. We find that this susceptibility diverges as T_c is approached from above, and has key features in common with the ``displacement-displacement susceptibility'' recently introduced to measure correlated particle motion in simulations of glass-forming liquids.

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Claudio Donati, Silvio Franz, Giorgio Parisi, Sharon C. Glotzer. 1999-12-16. Theory of Non-linear Susceptibility and Correlation Length in Glasses and Liquids. https://arxiv.org/abs/cond-mat/9905433

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