arXiv subjects

Pierfrancesco Urbani

Publications and source records attributed to Pierfrancesco Urbani.

60 records · Page 4Linked to original sources

arXiv2014

Statistical mechanics of the spherical hierarchical model with random fields

We study analytically the equilibrium properties of the spherical hierarchical model in the presence of random fields. The expression for the critical line separating a paramagnetic from a ferromagnetic phase is derived. The critical exponents characterising this phase transition are computed analytically and compared with those of the corresponding $D$-dimensional short-range model, leading to conclude that the usual mapping between one dimensional long-range models and $D$-dimensional short-range models holds exactly for this system, in contrast to models with Ising spins. Moreover, the critical exponents of the pure model and those of the random field model satisfy a relationship that mimics the dimensional reduction rule. The absence of a spin-glass phase is strongly supported by the local stability analysis of the replica symmetric saddle-point as well as by an independent computation of the free-energy using a renormalization-like approach. This latter result enlarges the class of random field models for which the spin-glass phase has been recently ruled out.

cond-mat.dis-nn↗

arXiv2014

Fractal free energy landscapes in structural glasses

Glasses are amorphous solids whose constituent particles are caged by their neighbors and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers. Here we show, using theory and numerical simulation, that the landscape is much rougher than is classically assumed. Deep in the glass, it undergoes a "roughness transition" to fractal basins. This brings about isostaticity at jamming and marginality of glassy states near jamming. Critical exponents for the basin width, the weak force distribution, and the spatial spread of quasi-contacts at jamming can be analytically determined. Their value is found to be compatible with numerical observations. This advance therefore incorporates the jamming transition of granular materials into the framework of glass theory. Because temperature and pressure control which features of the landscape are experienced, glass mechanics and transport are expected to reflect the features of the topology we discuss here. Hitherto mysterious properties of low-temperature glasses could be explained by this approach.

cond-mat.dis-nn↗

arXiv2013

Quantitative field theory of the glass transition

We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we study analytically the critical behavior of a set of four-points correlation functions from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find results that are consistent with numerical simulations.

cond-mat.dis-nn↗

arXiv2013

Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition

We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the Random First Order Transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis, and a further transition at higher pressures in which a glassy structure of micro-states is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Micro states that are small excitations of an amorphous matrix -- separated by low entropic or energetic barriers -- thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.

cond-mat.stat-mech↗

arXiv2013

Static replica approach to critical correlations in glassy systems

We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover we perform a one-loop computation in order to identify the region in which the mean field Gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the Hypernetted Chain approximation for the replicated liquid theory.

cond-mat.stat-mech↗

arXiv2012

A note on weakly discontinuous dynamical transitions

We analyze Mode Coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called "$A_3$" point. In these conditions structural relaxation and fluctuations appear to have universal form independent from the details of the system. The analysis of this limiting case suggests new ways for looking at the Mode Coupling equations in the general case.

cond-mat.stat-mech↗