arXiv subjects

Ada Altieri

Publications and source records attributed to Ada Altieri.

21 records · Page 2Linked to original sources

arXiv2017

Higher order corrections to the effective potential close to the jamming transition in the perceptron model

We analyze the perceptron model performing a Plefka-like expansion of the free energy. This model falls in the same universality class as hard spheres near jamming, allowing to get exact predictions in high dimensions for more complex systems. Our method enables to define an effective potential (or TAP free energy), namely a coarse-grained functional depending on the contact forces and the effective gaps between the particles. The derivation is performed up to the third order, with a particular emphasis on the role of third order corrections to the TAP free energy. These corrections, irrelevant in a mean-field framework in the thermodynamic limit, might instead play a fundamental role when considering finite-size effects. We also study the typical behavior of the forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. In our analysis, third order contributions vanish in the jamming limit, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the scalings emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

cond-mat.dis-nn↗

arXiv2016

The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential

We present a parallel derivation of the Thouless-Anderson-Palmer (TAP) equations and of an effective potential for the negative perceptron and soft sphere models in high dimension. Both models are continuous constrained satisfaction problems with a critical jamming transition characterized by the same exponents. Our analysis reveals that a power expansion of the potential up to the second order represents a successful framework to approach the jamming line from the SAT phase (the region of the phase diagram where at least one configuration verifies all the constraints), where the ground-state energy is zero. An interesting outcome is that close to jamming the effective thermodynamic potential has a logarithmic contribution, which turns out to be dominant in a proper scaling regime. Our approach is quite general and can be directly applied to other interesting models. Finally, we study the spectrum of small harmonic fluctuations in the SAT phase recovering the typical scaling $D(ω) \sim ω^2$ below the cutoff frequency but a different behavior characterized by a non-trivial exponent above it.

cond-mat.dis-nn↗

arXiv2015

Composite operators in Cubic Field Theories and Link Overlap Fluctuations in Spin-Glass Models

We present a complete characterization of the fluctuations and correlations of the squared overlap in the Edwards-Anderson Spin-Glass model in zero field. The analysis reveals that the energy-energy correlations (and thus the specific heat) have a different critical behavior than the fluctuations of the link overlap in spite of the fact that the average energy and average link overlap have the same critical properties. More precisely the link-overlap fluctuations are larger than the specific heat according to a computation at first order in the $6-ε$ expansion. An unexpected outcome is that the link-overlap fluctuations have a subdominant power-law contribution characterized by an anomalous logarithmic prefactor which is missing in the specific heat. In order to compute the $ε$ expansion we consider the problem of the renormalization of quadratic composite operators in a generic multicomponent cubic field theory: the results obtained have a range of applicability beyond spin-glass theory.

cond-mat.dis-nn↗