Publications

Order by: publication date number of citations

• Random features and polynomial rules

  Fabián Aguirre-López, Silvio Franz, Mauro Pastore

  SciPost Phys. 18, 039 (2025) · published 31 January 2025 | Toggle abstract · pdf

  Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance of random features models for generic supervised learning problems with Gaussian data. Our approach, built with tools from the statistical mechanics of disordered systems, maps the random features model to an equivalent polynomial model, and allows us to plot average generalization curves as functions of the two main control parameters of the problem: the number of random features $N$ and the size $P$ of the training set, both assumed to scale as powers in the input dimension $D$. Our results extend the case of proportional scaling between $N$, $P$ and $D$. They are in accordance with rigorous bounds known for certain particular learning tasks and are in quantitative agreement with numerical experiments performed over many order of magnitudes of $N$ and $P$. We find good agreement also far from the asymptotic limits where $D\to ∞$ and at least one between $P/D^K$, $N/D^L$ remains finite.

  3 citations

• Universal and non-universal large deviations in critical systems

  Ivan Balog, Bertrand Delamotte, Adam Rançon

  SciPost Phys. 18, 119 (2025) · published 2 April 2025 | Toggle abstract · pdf

  Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large $n$ limit, and Monte Carlo simulations, we investigate universal rare events of critical $O(n)$ systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cramér's series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics. We also discuss the ubiquity of this power-law corrections to the leading compressed-exponential decay in these tails in and out-of-equilibrium.

  3 citations

• Interfacially adsorbed bubbles determine the shape of droplets

  Alessio Squarcini, Antonio Tinti

  SciPost Phys. 15, 164 (2023) · published 16 October 2023 | Toggle abstract · pdf

  The characterization of density correlations in the presence of strongly fluctuating interfaces has always been considered a difficult problem in statistical mechanics. Here we study - by using recently developed exact field-theoretical techniques - density correlations for an interface with endpoints on a wall forming a droplet in 2D. Our framework applies to interfaces entropically repelled by a hard wall as well as to wetting transitions. In the former case bubbles adsorbed on the interface are taken into account by the theory which yields a systematic treatment of finite-size corrections to one- and two-point functions and show how these are related to Brownian excursions. Our analytical predictions are confirmed by Monte Carlo simulations without free parameters. We also determine one- and two-point functions at wetting by using integrable boundary field theory. We show that correlations are long ranged for entropic repulsion and at wetting. For both regimes we investigate correlations in momentum space by generalizing the notion of interface structure factor to semi-confined systems. Distinctive signatures of the two regimes manifest in the structure factor through a term that we identify on top of the capillary-wave one.

  2 citations

• Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class

  Marten Reehorst, Slava Rychkov, Benoit Sirois, Balt C. van Rees

  SciPost Phys. 18, 060 (2025) · published 19 February 2025 | Toggle abstract · pdf

  We study multiscalar theories with $\text{O}(N) × \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain $N_c(d)$ for $3 ≤ d < 4$. Our results show that $N_c> 3.78$ for $d = 3$. This favors the scenario that the physically relevant models with $N = 2,3$ in $d=3$ do not have a stable fixed point, indicating a first-order transition. Our result exemplifies how conformal windows can be rigorously constrained with modern numerical bootstrap algorithms.

  2 citations

• Associative bond swaps in molecular dynamics

  Simone Ciarella, Wouter G. Ellenbroek

  SciPost Phys. 12, 128 (2022) · published 12 April 2022 | Toggle abstract · pdf

  We implement a three-body potential to model associative bond swaps, and release it as part of the HOOMD-blue software. The use of a three-body potential to model swaps has been proven to be effective and has recently provided useful insights into the mechanics and dynamics of adaptive network materials such as vitrimers. It is elegant because it can be used in plain molecular dynamics simulations without the need for topology-altering Monte Carlo steps, and naturally represents typical physical features such as slip-bond behavior. It is easily tunable with a single parameter to control the average swap rate. Here, we show how associative bond swaps can be used to speed up the equilibration of systems that self-assemble by avoiding traps and pitfalls, corresponding to long-lived metastable configurations. Our results demonstrate the possibilities of these swaps not only for modeling systems that are associative by nature, but also for increasing simulation efficiency in other systems that are modellable in HOOMD-blue.

  2 citations

• Equilibration of quantum cat states

  Tony Jin

  SciPost Phys. 9, 004 (2020) · published 8 July 2020 | Toggle abstract · pdf

  We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in the mean, there exists a remnant of the initial quantum coherences visible in the strength of the fluctuations of the steady state. We back-up our analysis with numerical results obtained on the XXX spin chain with a random field along the z-axis in the ergodic regime and find good qualitative and quantitative agreement with the theory. We also present and discuss a framework where equilibrium quantities can be computed from general statistical ensembles without relying on microscopic details about the initial state, akin to the eigenstate thermalization hypothesis.

  2 citations

• Coarse-grained curvature tensor on polygonal surfaces

  Charlie Duclut, Aboutaleb Amiri, Joris Paijmans, Frank Jülicher

  SciPost Phys. Core 5, 011 (2022) · published 11 March 2022 | Toggle abstract · pdf

  Using concepts from integral geometry, we propose a definition for a local coarse-grained curvature tensor that is well-defined on polygonal surfaces. This coarse-grained curvature tensor shows fast convergence to the curvature tensor of smooth surfaces, capturing with accuracy not only the principal curvatures but also the principal directions of curvature. Thanks to the additivity of the integrated curvature tensor, coarse-graining procedures can be implemented to compute it over arbitrary patches of polygons. When computed for a closed surface, the integrated curvature tensor is identical to a rank-2 Minkowski tensor. We also provide an algorithm to extend an existing C++ package, that can be used to compute efficiently local curvature tensors on triangulated surfaces.

  2 citations

• Variation along liquid isomorphs of the driving force for crystallization

  Ulf R. Pedersen, Karolina Adrjanowicz, Kristine Niss, Nicholas P. Bailey

  SciPost Phys. 2, 022 (2017) · published 21 June 2017 | Toggle abstract · pdf

  We investigate the variation of the driving force for crystallization of a supercooled liquid along isomorphs, curves along which structure and dynamics are invariant. The variation is weak, and can be predicted accurately for the Lennard-Jones fluid using a recently developed formalism and data at a reference temperature. More general analysis allows interpretation of experimental data for molecular liquids such as dimethyl phthalate and indomethacin, and suggests that the isomorph scaling exponent $\gamma$ in these cases is an increasing function of density, although this cannot be seen in measurements of viscosity or relaxation time.

  2 citations

• On the topology of solutions to random continuous constraint satisfaction problems

  Jaron Kent-Dobias

  SciPost Phys. 18, 158 (2025) · published 15 May 2025 | Toggle abstract · pdf

  We consider the set of solutions to $M$ random polynomial equations whose $N$ variables are restricted to the $(N-1)$-sphere. Each equation has independent Gaussian coefficients and a target value $V_0$. When solutions exist, they form a manifold. We compute the average Euler characteristic of this manifold in the limit of large $N$, and find different behavior depending on the target value $V_0$, the ratio $\alpha=M/N$, and the variances of the coefficients. We divide this behavior into five phases with different implications for the topology of the solution manifold. When $M=1$ there is a correspondence between this problem and level sets of the energy in the spherical spin glasses. We conjecture that the transition energy dividing two of the topological phases corresponds to the energy asymptotically reached by gradient descent from a random initial condition, possibly resolving an open problem in out-of-equilibrium dynamics. However, the quality of the available data leaves the question open for now.

  2 citations

• Python-JAX-based fast Stokesian dynamics

  Kim William Torre, Raoul D. Schram, Joost de Graaf

  SciPost Phys. Codebases 56 (2025) · published 30 June 2025 | Toggle abstract · pdf

  Stokesian Dynamics (SD) is a powerful computational framework for simulating the motion of particles in a viscous Newtonian fluid under Stokes-flow conditions. Traditional SD implementations can be computationally expensive as they rely on the inversion of large mobility matrices to determine hydrodynamic interactions. Recently, however, the simulation of thermalized systems with large numbers of particles has become feasible [Fiore and Swan, J. Fluid Mech. 878, 544 (2019)]. Their "fast Stokesian dynamics" (FSD) method leverages a saddle-point formulation to ensure overall scaling of the algorithm that is linear in the number of particles $\mathcal{O}(N)$; performance relies on dedicated graphics-processing-unit computing. Here, we present a different route toward implementing FSD, which instead leverages the Just-in-Time (JIT) compilation capabilities of Google JAX. We refer to this implementation as JFSD and perform benchmarks on it to verify that it has the right scaling and is sufficiently fast by the standards of modern computational physics. In addition, we provide a series of physical test cases that help ensure accuracy and robustness, as the code undergoes further development. Thus, JFSD is ready to facilitate the study of hydrodynamic effects in particle suspensions across the domains of soft, active, and granular matter.

  2 citations