arXiv subjects

Luca Di Carlo

Publications and source records attributed to Luca Di Carlo.

16 recordsLinked to original sources

arXiv2026

Non-equilibrium coupling to a diffusing density breaks Ising universality

The Ising universality class is remarkably robust to non-equilibrium perturbations, which generically flow to zero under renormalization. We show that this robustness fails when an order parameter is coupled nonreciprocally to a conserved diffusive density. Below $d_c=4$, the renormalization group flows to a fast-diffusion fixed point at which the density acts as a long-range multiplicative noise, producing a novel universality class. The non-equilibrium nature of the fixed point is manifest in the large-scale violation of the fluctuation-dissipation relations, reflected in a splitting of the scaling exponents of the two-point correlation and response functions--a measurable hallmark of non-equilibrium critical fluctuations. A two-loop calculation establishes the stability of this fixed point but yields a small correction-to-scaling exponent $ω\approx0.020$ in $d=3$, implying strong finite-size corrections. An all-orders modified Harris criterion $ν>2/(d+z-2)$ confirms that the BIM fixed point governs criticality in $d=3$, with Ising universality recovered only at $d=2$.

cond-mat.stat-mech↗

arXiv2026

Non-equilibrium phase transition in the Brownian Ising Model: field theory, renormalization group, and exact results

We present a complete field-theoretical renormalization-group (RG) analysis of the Brownian Ising Model (BIM), in which a $\mathbb{Z}_2$ order parameter is coupled to a passive conserved density, breaking detailed balance. Using the Martin-Siggia-Rose formalism and an $ε=4-d$ expansion, we show that this density-order parameter coupling is RG-relevant below four dimensions and drives the system to a new non-equilibrium fixed point, distinct from the Ising universality class. Critical exponents are computed at lowest nontrivial order, some of which require a dedicated two-loop analysis. At large scales, the density acts as an effective noise that is white in time but long-range in space, enhancing order-parameter fluctuations and producing a negative anomalous dimension $η$. A defining feature of the new class is that the correlation and response functions acquire different anomalous dimensions, $η\neq 2 - γ/ ν$ - a direct, observable signature of fluctuation-dissipation-theorem violation at large scales that cannot occur in equilibrium. We also find a small correction-to-scaling exponent, implying large preasymptotic corrections that must be accounted for in numerical and experimental tests. We further derive a set of relations among renormalization factors that hold to all orders in perturbation theory, following from the linearity of the density dynamics and an emergent shift symmetry. These yield an exact scaling relation $ν= 2/(d+z-2)$ at the BIM fixed point and establish that the Ising universality class, as well as that of quenched diluted-Ising, is unstable in $d=3$. This establishes the BIM fixed point as the unique infrared attractor for any nonzero diffusion constant.

cond-mat.stat-mech↗

arXiv2026

Entropic Confinement and Mode Connectivity in Overparameterized Neural Networks

Modern neural networks exhibit a striking property: basins of attraction in the loss landscape are often connected by low-loss paths, yet optimization dynamics generally remain confined to a single convex basin and rarely explore intermediate points. We resolve this paradox by identifying entropic barriers arising from the interplay between curvature variations along these paths and noise in optimization dynamics. Empirically, we find that curvature systematically rises away from minima, producing effective forces that bias noisy dynamics back toward the endpoints - even when the loss remains nearly flat. These barriers persist longer than energetic barriers, shaping the late-time localization of solutions in parameter space. Our results highlight the role of curvature-induced entropic forces in governing both connectivity and confinement in deep learning landscapes.

cs.LG↗

arXiv2026

Soft Quantization: Model Compression Via Weight Coupling

We show that introducing short-range attractive couplings between the weights of a neural network during training provides a novel avenue for model quantization. These couplings rapidly induce the discretization of a model's weight distribution, and they do so in a mixed-precision manner despite only relying on two additional hyperparameters. We demonstrate that, within an appropriate range of hyperparameters, our "soft quantization'' scheme outperforms histogram-equalized post-training quantization on ResNet-20/CIFAR-10. Soft quantization provides both a new pipeline for the flexible compression of machine learning models and a new tool for investigating the trade-off between compression and generalization in high-dimensional loss landscapes.

cs.LG↗

arXiv2025

Informational Memory Shapes Collective Behavior in Intelligent Swarms

We present an experimental and theoretical study of 2-D swarms in which collective behavior emerges from both direct local mechanical coupling between agents and from the exchange and processing of information between agents. Each agent, an air-table drone endowed with internal memory and a binary decision variable, updates its state by integrating a time series of memories of local past collisions. This internal computation transforms the drone swarm into a dynamical information network in which history-dependent feedback drives spontaneous complete spin polarization, pitchfork bifurcated spin collectives, and chaotic switching between collective states. By tuning the depth of memory and the decision algorithm, we uncover a memory-induced phase transition that breaks spin symmetry at the population level. A minimal theoretical model maps these dynamics onto an effective potential landscape sculpted by informational feedback, revealing how temporally correlated computation can replace instantaneous forces as the driver of collective organization, informed by experiments. These results position physically interacting drone swarms as a model system for exploring the physics of informational drone ensembles whose emergent behavior arises from the interplay between physical interaction and information processing.

physics.soc-ph↗

arXiv2025

Neural subspaces, minimax entropy, and mean-field theory for networks of neurons

Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural populations. Correlations in the brain are typically weak but widespread, suggesting that a mean-field approach might be effective in describing real neural populations, and we explore a hierarchy of maximum entropy models guided by this idea. We begin with models that match only the mean and variance of the total population activity, and extend to models that match the experimentally observed mean and variance of activity along multiple projections of the neural state. Confronted by data from several different brain regions, these models are driven toward a first-order phase transition, characterized by the presence of two nearly degenerate minima in the energy landscape, and this leads to predictions in qualitative disagreement with other features of the data. To resolve this problem we introduce a novel class of models that constrain the full probability distribution of activity along selected projections. We develop the mean-field theory for this class of models and apply it to recordings from 1000+ neurons in the mouse hippocampus. This 'distributional mean--field' model provides an accurate and consistent description of the data, offering a scalable and principled approach to modeling complex neural population dynamics.

physics.bio-ph↗

arXiv2025

Extended mean-field theories for networks of real neurons

If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the patterns of activity in networks of real neurons. An extended mean-field theory that matches the distribution of collective variables is at least consistent, though shows signs that these networks are poised near a critical point, in agreement with other observations. These results suggest a path to analysis of emerging data on ever larger numbers of neurons.

physics.bio-ph↗

arXiv2025

Monte Carlo, blocking, and inference: How to measure the renormalization group flow

Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of scaling theory. Most courses on phase transitions focus on scaling and critical exponents, while less attention is paid to universality, renormalization group flow, and the existence of a unique fixed point, which are the ultimate reasons why scaling theory is so effective in describing continuous phase transitions. We use a combination of Monte Carlo simulations and real space renormalization group theory to determine the renormalization group flow and to show the existence of a universal fixed point in the context of the ferromagnetic Ising model.

cond-mat.stat-mech↗

arXiv2024

The off-equilibrium Kinetic Ising model: The Metric Case

We investigate the critical behavior of the Kinetic Ising model with non-reciprocal nearest neighbors interactions. A finite-size scaling study suggests that the model belongs to the Ising universality class. We characterize the off-equilibrium behavior of the model by measuring the entropy production rate and by studying the coarsening dynamics, which shows a super-diffusive relaxation. A coarse-grained equation of motion is in compelling agreement with the numerical findings. A one-loop renormalization group calculation shows that the model belongs to the Model A universality class.

cond-mat.stat-mech↗

arXiv2024

Maximum entropy models for patterns of gene expression

New experimental methods make it possible to measure the expression levels of many genes, simultaneously, in snapshots from thousands or even millions of individual cells. Current approaches to analyze these experiments involve clustering or low-dimensional projections. Here we use the principle of maximum entropy to obtain a probabilistic description that captures the observed presence or absence of mRNAs from hundreds of genes in cells from the mammalian brain. We construct the Ising model compatible with experimental means and pairwise correlations, and validate it by showing that it gives good predictions for higher-order statistics. We notice that the probability distribution of cell states has many local maxima. By labeling cell states according to the associated maximum, we obtain a cell classification that agrees well with previous results that use traditional clustering techniques. Our results provide quantitative descriptions of gene expression statistics and interpretable criteria for defining cell classes, supporting the hypothesis that cell classes emerge from the collective interaction of gene expression levels.

physics.bio-ph↗

arXiv2022

Natural Swarms in $\bf 3.99$ Dimensions

The dynamical critical exponent $z$ of natural swarms of insects is calculated using the renormalization group to order $ε= 4-d$. A novel fixed point emerges, where both activity and inertia are relevant. In three dimensions the critical exponent at the new fixed point is $z = 1.35$, in agreement with both experiments ($1.37 \pm 0.11$) and numerical simulations ($1.35 \pm 0.04$).

cond-mat.stat-mech↗

arXiv2022

Evidence of fluctuation-induced first-order phase transition in active matter

We study the properties of the Malthusian Toner-Tu theory in its near ordering phase. Because of the birth/death process, characteristic of this Malthusian model, density fluctuations are partially suppressed. We study this model using the perturbative renormalization group. At one loop we find that the renormalization group flow drives the system in an unstable region, suggesting a fluctuation-induced first-order phase transition.

cond-mat.soft↗

arXiv2020

Equilibrium to off-equilibrium crossover in homogeneous active matter

We study the crossover between equilibrium and off-equilibrium dynamical universality classes in the Vicsek model near its ordering transition. Starting from the incompressible hydrodynamic theory of Chen et al \cite{chen2015critical}, we show that increasing the activity leads to a renormalization group (RG) crossover between the equilibrium ferromagnetic fixed point, with dynamical critical exponent $z = 2$, and the off-equilibrium active fixed point, with $z = 1.7$ (in $d=3$). We run simulations of the classic Vicsek model in the near-ordering regime and find that critical slowing down indeed changes with activity, displaying two exponents that are in remarkable agreement with the RG prediction. The equilibrium-to-off-equilibrium crossover is ruled by a characteristic length scale beyond which active dynamics takes over. Such length scale is smaller the larger the activity, suggesting the existence of a general trade-off between activity and system's size in determining the dynamical universality class of active matter.

cond-mat.stat-mech↗

arXiv2019

Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks

We introduce a new ferromagnetic model capable of reproducing one of the most intriguing properties of collective behaviour in starling flocks, namely the fact that strong collective order of the system coexists with scale-free correlations of the modulus of the microscopic degrees of freedom, that is the birds' speeds. The key idea of the new theory is that the single-particle potential needed to bound the modulus of the microscopic degrees of freedom around a finite value, is marginal, that is has zero curvature. We study the model by using mean-field approximation and Monte Carlo simulations in three dimensions, complemented by finite-size scaling analysis. While at the standard critical temperature, $T_c$, the properties of the marginal model are exactly the same as a normal ferromagnet with continuous symmetry-breaking, our results show that a novel zero-temperature critical point emerges, so that in its deeply ordered phase the marginal model develops divergent susceptibility and correlation length of the modulus of the microscopic degrees of freedom, in complete analogy with experimental data on natural flocks of starlings.

cond-mat.stat-mech↗

arXiv2019

Renormalization group crossover in the critical dynamics of field theories with mode coupling terms

Motivated by the collective behaviour of biological swarms, we study the critical dynamics of field theories with coupling between order parameter and conjugate momentum in the presence of dissipation. By performing a dynamical renormalization group calculation at one loop, we show that the violation of momentum conservation generates a crossover between a conservative yet IR-unstable fixed point, characterized by a dynamic critical exponent $z=d/2$, and a dissipative IR-stable fixed point with $z=2$. Interestingly, the two fixed points have different upper critical dimensions. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system, characterized by a crossover exponent $κ=4/d$. Such crossover is regulated by a conservation length scale, $\mathcal R_0$, which is larger the smaller the dissipation: beyond $\mathcal R_0$ the dissipative fixed point dominates, while at shorter distances dynamics is ruled by the conservative fixed point and critical exponent, a behaviour which is all the more relevant in finite-size systems with weak dissipation. We run numerical simulations in three dimensions and find a crossover between the exponents $z=3/2$ and $z=2$ in the critical slowing down of the system, confirming the renormalization group results. From the biophysical point of view, our calculation indicates that in finite-size biological groups mode-coupling terms in the equation of motion can significantly change the dynamical critical exponents even in the presence of dissipation, a step towards reconciling theory with experiments in natural swarms. Moreover, our result provides the scale within which fully conservative Bose-Einstein condensation is a good approximation in systems with weak symmetry-breaking terms violating number conservation, as quantum magnets or photon gases.

cond-mat.stat-mech↗

arXiv2019

Dynamical renormalization group approach to the collective behaviour of swarms

We study the critical behaviour of a model with non-dissipative couplings aimed at describing the collective behaviour of natural swarms, using the dynamical renormalization group. At one loop, we find a crossover between a conservative yet unstable fixed point, characterized by a dynamical critical exponent $z=d/2$, and a dissipative stable fixed point with $z=2$, a result we confirm through numerical simulations. The crossover is regulated by a conservation length scale that is larger the smaller the effective friction, so that in finite-size biological systems with low dissipation, dynamics is ruled by the conservative fixed point. In three dimensions this mechanism gives $z=3/2$, a value significantly closer to the experimental result $z\approx 1$ than the value $z\approx 2$ found in fully dissipative models, either at or off equilibrium. This result indicates that non-dissipative dynamical couplings are necessary to develop a theory of natural swarms fully consistent with experiments

cond-mat.stat-mech↗