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Low frequency quasi-localized modes of amorphous glasses appear to exhibituniversal density of states, depending on the frequencies as $D(\omega) \sim\omega^4$. To date various models of glass formers with short range binaryinteraction, and network glasses with both binary and ternary interactions,were shown to conform with this law. In this paper we examine granularamorphous solids with long-range electrostatic interactions, and find that theyexhibit the same law. To rationalize this wide universality class we return toa model proposed by Gurevich, Parshin and Schober (GPS) and analyze itspredictions for interaction laws with varying spatial decay, exploring thiswider than expected universality class. Numerical and analytic results areprovided for both the actual system with long range interaction and for the GPSmodel.

Robustness of Density of Low Frequency States in Amorphous Solids