Within the frame of mode-coupling theory for ideal glass transitions, asymptotic laws for higher-order glass-transition singularities are derived. In contrary to the simple liquid-glass transition where power laws describe the dynamics, logarithmic decay laws determine the behavior of higher-order singularities. Expansions in powers and inverse powers of the logarithm of time for the correlation functions are introduced and tested in schematic models. Upon application to systems with short-ranged attraction, surfaces are found in control-parameter space where corrections to the leading logarithmic decay vanish. When crossing these surfaces, the correlation functions shows a characteristic change from concave to convex behavior in semilogarithmic representation. A similar scenario arises when changing the wave vector or when considering the mean-squared displacement while variation of parameters in double-logarithmic representation
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Within the frame of mode-coupling theory for ideal glass transitions, asymptotic laws for higher-order glass-transition singularities are derived. In contrary to the simple liquid-glass transition where power laws describe the dynamics, logarithmic decay laws determine the behavior of higher-order singularities. Expansions in powers and inverse powers of the logarithm of time for the correlation functions are introduced and tested in schematic models. Upon application to systems with short-range...
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