Abstract
We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.
Highlights
We investigate the potential energy landscape (PEL) of soft spheres interacting through a linear ramp potential, obtained by setting α = 1, above the jamming transition point
In this work we have described the emergence of a new critical phase obtained when linear spheres are compressed above the jamming point
The criticality of local minima of the PEL of linear soft spheres is described by a set of power laws controlling the positive and negative gap distributions as well as contact forces
Summary
Since more than twenty years, the ideal jamming points of systems of frictionless spheres have shaped our thinking of low temperature glasses, suggested principles underlying amorphous rigidity, and provided mechanisms to rationalize low energy excitations in glasses [1,2]. Marginal stability implies power law behavior of the distribution of these quantities at small argument [9,10] and predicts a non trivial relation between the corresponding exponents [12]. These exponents have been computed exactly in [13, 14] and have been shown to agree -within numerical precision- with numerical simulations of hard and soft spheres in various physical dimensions [15]. The emerging marginal stability is richer that the one appearing at the boundary jamming transition, with additional system spanning non-linear excitations
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