arXiv subjects

Mattia Scandolo

Publications and source records attributed to Mattia Scandolo.

8 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 $\omega\approx0.020$ in $d=3$, implying strong finite-size corrections. An all-orders modified Harris criterion $\nu>2/(d+z-2)$ 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 $\epsilon=4-d$ 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 $\eta$. A defining feature of the new class is that the correlation and response functions acquire different anomalous dimensions, $\eta \neq 2 - \gamma / \nu$ - 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 $\nu = 2/(d+z-2)$ 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

Information bounds the robustness of self-organized systems

Self-organized systems, from synthetic nanostructures to developing organisms, are composed of fluctuating units capable of forming robust functional structures despite noise. Here, we ask: are there fundamental bounds on the robustness of noisy self-organized systems? By viewing self-organization as noisy encoding, we prove that the positional information capacity of short-range classical systems with discrete states obeys a bound reminiscent of area laws for quantum information. We illustrate this principle with lattice models whose dynamics is captured by continuum models derived using exact coarse-graining techniques and validated through Dynamical Renormalization Group calculations. The universal bound is saturated by fine-tuning transport coefficients, which can be rationalized in the continuum limit upon considering the effects of boundaries on domain wall dynamics. We illustrate how this limit can be bypassed when long-range correlations are present by investigating a wave-pinning model motivated by biological mechanisms. In this class of models, global constraints reduce the need for fine-tuning by providing effective integral feedback. Our work identifies fundamental limits for the ability of natural and synthetic microsystems to self-assemble into patterns and rationalizes them on purely information-theoretic grounds.

physics.bio-ph↗

arXiv2025

Spin-Waves without Spin-Waves: A Case for Soliton Propagation in Starling Flocks

Collective turns in starling flocks propagate linearly with negligible attenuation, indicating the existence of an underdamped sector in the dispersion relation. Beside granting linear propagation of the phase perturbations, the real part of the frequency should also yield a spin-wave form of the unperturbed correlation function. However, new high-resolution experiments on real flocks show that underdamped traveling waves coexist with an overdamped Lorentzian correlation. Theory and experiments are reconciled once we add to the dynamics a Fermi-Pasta-Ulam-Tsingou term.

cond-mat.stat-mech↗

arXiv2023

Active Ising Models of Flocking: A Field-Theoretic Approach

Using an approach based on Doi-Peliti field theory, we study several different Active Ising Models (AIMs), in each of which collective motion (flocking) of self-propelled particles arises from the spontaneous breaking of a discrete symmetry. We test the predictive power of our field theories by deriving the hydrodynamic equations for the different microscopic choices of aligning processes that define our various models. At deterministic level, the resulting equations largely confirm known results, but our approach has the advantage of allowing systematic generalization to include noise terms. Study of the resulting hydrodynamics allows us to confirm that the various AIMs share the same phenomenology of a first order transition from isotropic to flocked states whenever the self propulsion speed is nonzero, with an important exception for the case where particles align only pairwise locally. Remarkably, this variant fails entirely to give flocking -- an outcome that was foreseen in previous work, but is confirmed here and explained in terms of the scalings of various terms in the hydrodynamic limit. Finally, we discuss our AIMs in the limit of zero self-propulsion where the ordering transition is continuous. In this limit, each model is still out of equilibrium because the dynamical rules continue to break detailed balance, yet it has been argued that an equilibrium universality class (Model C) prevails. We study field-theoretically the connection between our AIMs and Model C, arguing that these particular models (though not AIMs in general) lie outside the Model C class. We link this to the fact that in our AIMs without self propulsion, detailed balance is not merely still broken, but replaced by a different dynamical symmetry in which the dynamics of the particle density is independent of the spin state.

cond-mat.stat-mech↗

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↗

arXiv2021

Dynamical renormalization group for mode-coupling field theories with solenoidal constraint

The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles' velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields - density, velocity and spin - has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups.

cond-mat.stat-mech↗