Free-energy Landscape And Critical Response In Structural Glasses Upon Jamming

Most materials can form glasses when their liquids are cooled(or compressed)sufficiently fast to avoid crystallization.As the dynamics of liquids slow down rapidly,they may end up in disordered solids that can bear loads such as shear.Such a phe-nomenon is known as the glass transition.Since the structural symmetry breaking is absent in glass transition,the order parameters of the related thermodynamical theories are still very controversial,and it is far from reaching an agreement by far.In contrast to the small changes in structure,the relaxation time increases by dozens of magnitude upon forming glasses.Some physicists thus suggest that the glass transition is purely dynamic.Although there are many theories,most of them remain at the level of phe-nomena and apply only to some special cases and cannot give verifiable predictions.On the other hand,owing to complex competitive factors and non-equilibrium nature in real glasses,it is difficult to verify a theory accurately in simulations and experiments.Another branch of disorder solids research is the jamming transition,at which the loose collections of athermal particles transform into rigid solids.In simulations,the jam-ming transition is found to be critical in some situations for non-trivial scaling relations and critical response.Some of the critical exponents are repeatedly validated and are with high precision.For decades,the underlying microscopic mechanism of jamming criticality was lacking,despite phenomenological explanations.Another long-standing issue is the relationship between glasses and jammed states,considering that both of them are disordered solids.Recently,great progress has been made on these issues.The mean-field the-ory(MFT)with the amorphous order predicts a Gardner phase transition deep inside glasses.Upon compressing(or cooling),the states transform from metastable phase into marginal and ultrametric Gardner phase spontaneously.By attributing the jam-ming to the infinite-pressure Gardner phase,MFT predicts the correct jamming critical exponents from the first principle.However,Gardner phase transition is not expected in two dimension(2d)theoretically.And this seems to contradict the experimental fact that jamming criticality presents in all d?2 and is nearly independent on dimension.To address the matter,we numerically study the 2d hard disk glasses and develop novel tools to analyze the phase space.We find a sharp Gardner transition in hard disk glasses,although the real phase transition is avoided.As the pressure increases above a thresh-old,the order parameters become long-ranged correlated.When the system sizes are smaller than the correlation lengths,the phase spaces are ultrametric and MFT is ap-proximately accurate.As for the self-averaged systems,we find that the free-energy landscapes remain hierarchical,despite the loss of the ultrametricity.Therefore,the de-scriptions of the Gardner phase by MFT can be useful in the physical dimension,even when the phase transition is avoided.We also close the debates about two other con-troversial issues,the Mermin-Wagner fluctuations(MWFs)and the localized defects(LDs).We show that MWFs just play the role of background and LDs do not stem from the degenerate Gardner physics.In terms of jamming transition,we study the response to the self-propulsion in the vicinity of jamming.The active matter has received extensive attention for potential applications recently.One of the typical features of active matter is the local energy input.And it can be studied in a simple model of self-propelled particles(SPPs).We consider the zero-temperature limit of SPPs,that is,the particles propelled by constant forces f pointing to randomly assigned and fixed directions.Different from the previous studies of shear,the loads here are highly local.When f is smaller than the yield force fy,SPPs are statically jammed,otherwise,they flow forever.We find that the yield force fy increases with the packing fraction and exhibits non-trivial finite-size scaling.For the fluids,we propose using R=v/f as the response function,with v is the average velocity.It turns out that R displays critical scaling nicely,analogous to the behaviors of inverse shear viscosity.In summary,for the first time,our results show that the response to self-propulsion can be critical in the jamming transition and self-propulsion may play a role similar to shear stress.