arXiv subjects

Leticia F. Cugliandolo

Publications and source records attributed to Leticia F. Cugliandolo.

At least 19 recordsLinked to original sources

arXiv2026

Ground-state properties of the two-dimensional SWAP spin-glass ensemble

We study the recently introduced SWAP ensemble for Ising spin-glasses, where the spins obtain varying lengths, with length scale $Δ\in [0, 2]$. The lengths can be exchanged in the spirit of the SWAP algorithm for glassy poly-disperse hard-sphere systems. Using an annealing schedule, if the annealing is slow enough, ground states of the corresponding Ising Hamiltonian, where the spin lengths are incorporated into the bonds, can be obtained with high probability. We prove this statement for two-dimensional systems with sizes of up to $L^2=1024^2$ spins by comparison with exact ground states obtained by using graph matching algorithms. In particular, we analyze the nature of the obtained realizations of the disorder by calculating exact zero-temperature domain-wall energies, from exact ground state calculations using periodic and anti-periodic boundary conditions. For medium or large values of $Δ$, e.g. $Δ=1$, the realizations turn ferromagnetic if the annealing is slow enough, i.e., they lose their zero-temperature spin-glass property. If $Δ$ is small, the realizations remain glassy, but the SWAP annealing does not easily find a true ground state.

cond-mat.dis-nn↗

arXiv2026

Coupling spherical p-spin systems

Spherical p-spin models provide a mean-field framework for glassy dynamics. Coupling such systems opens a controlled way to probe how they evolve jointly, develop cross correlations, and possibly share common aging scales. We study spherical p-spin systems with site-independent inter-system couplings and generally correlated quenched disorders. We derive closed multi-subsystem two-time equations for correlations, responses, and spherical constraints. A marginal one-step replica-symmetry-breaking construction provides static benchmarks for overlap plateaux, aging crossover scales, and effective temperatures. We then specialize to two ferromagnetically coupled p=3 systems and compare dynamical data with marginal 1RSB predictions. Independent quenched disorders reduce the equal-time correlation between the systems below its disorder-free value, while correlated disorders enhance it. For sufficiently strong coupling, finite-time fluctuation-dissipation estimates within and between the systems are compatible with a common effective temperature even when one or both subsystems would equilibrate as a paramagnet in isolation. This common value lies above the effective temperatures that the constituent systems would have separately and increases with disorder correlation and coupling strength. The marginal 1RSB value T/m captures these trends but is slightly below the finite-time dynamical estimate. For weak coupling, the dynamical results instead suggest that two aging regimes develop for each system, with partial equilibration within each. We perform a marginal replica analysis with two-step breaking, whose predictions compare favorably with the numerical measurements. Our numerical accuracy is insufficient to determine whether the observed finite-time crossover will eventually become a sharp transition.

cond-mat.dis-nn↗

arXiv2026

Phase Diagram and Critical Behaviour of the Two-Dimensional Potts Model with Long-Range Quenched Disorder

We study the phase diagram and critical properties of the $q = 3$ and $q = 8$ Potts models with spatially correlated disorder governed by a power-law decay with exponent $a$. Building on the phase diagram proposed by Chippari et al. [3], where a transition from finite-disorder to infinite-disorder fixed points was identified as a function of a, we refine this picture by using wrapping probabilities of Fortuin-Kasteleyn clusters. Furthermore, using magnetic observables, we clarify the physical origin of the double-peak structure in the magnetic susceptibility and establish the validity of the hyper-scaling relation across all investigated regimes.

cond-mat.stat-mech↗

arXiv2026

Percolation and criticality of systems with competing interactions on Bethe lattices: limitations and potential strengths of cluster schemes

The random clusters introduced by Fortuin and Kasteleyn (FK) and analyzed by Coniglio and Klein (CK) for Ising and related models have led first Swendsen and Wang and then Wolff to formulate remarkably efficient Markov chain Monte Carlo sampling schemes that weaken the critical slowing down. In frustrated models, however, no standard way to produce a comparable gain at small frustration -- let alone efficiently sample the large frustration regime -- has yet been identified. In order to understand why formulating appropriate cluster criteria for frustrated models has thus far been elusive, we here study minimal short-range attractive and long-range repulsive as well as spin-glass models on Bethe lattices. Using a generalization of the CK approach and the cavity-field method, the appropriateness and limitations of the FK--CK type clusters are identified. We find that a standard, constructive cluster scheme is then inoperable, and that the frustration range over which generalized FK--CK clusters are even definable is finite. These results demonstrate the futility of seeking constructive cluster schemes for frustrated systems but leaves open the possibility that alternate approaches could be devised.

cond-mat.stat-mech↗

arXiv2026

Large deviations in the many-body localization transition: The case of the random-field XXZ chain

The effect of rare system-wide resonances in the many-body localization (MBL) transition has recently attracted significant attention. They are expected to play a prominent role in the stability of the MBL phase, prompting the development of new theoretical frameworks to properly account for their statistical weight. We employ a method based on an analogy with mean-field disordered glassy systems to characterize the statistics of transmission amplitudes between distant many-body configurations in Hilbert space, and apply it to the random-field XXZ spin chain. By introducing a Lagrange multiplier, which formally plays the role of an effective temperature controlling the influence of extreme outliers in the heavy-tailed distribution of propagators, we identify three distinct regimes: (i) an ergodic phase with uniform spreading in Hilbert space, (ii) an intermediate regime where delocalization is driven by rare, disorder-dependent long-range resonances, and (iii) a robust MBL phase where such resonances cannot destabilize localization. We derive a finite-size phase diagram in the disorder--interaction plane both in the spin and in the Anderson basis that quantitatively agrees with recent numerical results based on real-space spin-spin correlation functions. We further demonstrate that even infinitesimal interactions can destroy the Anderson insulator at finite disorder, with the critical disorder remaining finite down to small interaction strengths. By visualizing resonant transmission pathways on the Hilbert space graph, we provide a complementary perspective to real-space and spectral probes, revealing how the destabilization of the MBL phase at finite sizes stems from the emergence of resonant paths that become progressively rarer and shorter-ranged deep in the localized phase.

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arXiv2026

Level statistics in the fractal phase of generalized Rosenzweig--Porter models

The Rosenzweig--Porter (RP) random matrix ensemble has emerged as a minimal model for the integrability-to-chaos crossover in quantum many-body systems. Its phase diagram features a region with fractal eigenstates, exhibiting intermediate spectral and localization properties between the fully localized and fully delocalized regimes. In this work, we explore several generalizations of the RP model and determine their level statistics at the scale of the Thouless energy $E_T$, which characterizes the crossover. Using tools from free probability theory and the replica method, we compute the full counting statistics in the limit of large system size, and show that it takes a simple, universal scaling form around $E_T$, shared across all variations of the model. We validate our analytical predictions using exact numerical diagonalization of large samples, and large-deviation algorithms that resolve the full counting statistics down to probabilities as low as $10^{-40}$. We also contrast our predictions with measurements on the quantum random energy model, which is the simplest model displaying many-body localization.

cond-mat.dis-nn↗

arXiv2026

Hamiltonian flocks: Time-Reversal Symmetry and its consequences

The fluctuation-dissipation theorem is a hallmark of equilibrium systems that stems from their time-reversal symmetry. In many non-equilibrium systems, in particular active ones, extensions and explicit violations of this theorem are used to assess their ''distance'' to equilibrium. In Hamiltonian flocks, conservative yet non-Galilean models of polar liquids, previous work reported collective motion without the activity that usually underlies it. In this paper, we show that this model obeys a generalized time-reversal symmetry that yields a fluctuation-dissipation theorem that mixes position and polarity degrees of freedom. Due to the oddness of spin under time reversal, the system also obeys Onsager-Casimir reciprocity rather than standard Onsager relations. The coupling also induces rich spin orientation dynamics, including a non-trivial diffusion constant at long times. Finally, we show that considering the naïve time-reversal operation rather than the generalized one that leaves the system invariant leads to a spurious entropy production rate, that could be wrongly interpreted as a distance to equilibrium. Our findings suggest looking for possible extensions of time-reversal symmetry in active-looking systems, which may lead to yet unknown generalizations of the fluctuation-dissipation theorem.

cond-mat.stat-mech↗

arXiv2026

Geometry and localization: Probing Localization Landscape Theory on the Bethe Lattice

The Localization Landscape Theory (LLT) offers a classical analogy for understanding Anderson localization through an effective confining potential, whose percolation threshold has been proposed to mark the mobility edge. While this correspondence shows striking numerical agreement in three dimensions, its theoretical foundations remain an open question. In this work, we extend the analysis of the LLT on the Bethe lattice presented in~\cite{Tonetti2026}. In this setting in both the Anderson localization transition and the LLT percolation problem admit exact solutions. Our analysis reveals that the two transitions are distinct, with markedly different critical behaviors. Notably, the LLT percolation transition falls into the standard mean-field universality class, in sharp contrast with the unconventional critical behavior of the Anderson transition on the Bethe lattice. Nonetheless, the LLT framework reproduces several exact results, capturing nontrivial features of the very low-disorder regime: it predicts the position of the isolated eigenvalue, the minimal disorder at which both the LLT percolation curve and the mobility edge first appear, and the Aizenman--Warzel lower bound for localization. We also study the dependence of the LLT percolation threshold on the energy shift, evaluate the LLT prediction for the Density of States, and derive several results on the statistical properties of the variables controlling the problem. Finally, we develop an extreme-value analysis showing that the LLT prediction for the Density of States overestimates the amplitude of the tails close to the boundary of the continuous spectrum. These findings provide an exact analytical benchmark showing that, despite its geometric appeal, the LLT does not generally reproduce the quantum critical properties of Anderson localization, while still offering a powerful tool to understand its very low-disorder regime.

cond-mat.dis-nn↗

arXiv2026

Critical quench dynamics of Wegner's $\mathbb{Z}_2$ gauge model: a geometric perspective

Wegner's $\mathbb{Z}_2$ gauge model is the earliest formulation of pure lattice gauge theory and predicts the topological nature of the confinement-deconfinement transition. In three dimensions ($D=3$), the equilibrium critical behavior of the model is understood in terms of geometrically defined objects, namely loop excitations and Fortuin-Kasteleyn (FK) clusters. This work investigates the critical quench dynamics of this model from a geometric perspective, following quenches from both a high-temperature percolation phase and the zero-temperature ground state. Using time-dependent finite-size scaling analysis, we find that the critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent $z_{\rm p} \simeq 2.6$, consistent with that associated with the energy density, $z_{\rm c}$. Importantly, the value of $z_{\rm p}$ is robust with respect to the initial quench condition and the choice of geometrical objects. Furthermore, we provide a detailed characterization of the kinetics of different geometrical objects during the evolution from the percolation phase. Notably, we observe that the quench dynamics obeys dynamic scaling in terms of a growing lengthscale, $ξ_{\rm p}(t) \sim t^{1/z_{\rm p}}$, despite the absence of a local order parameter.

cond-mat.stat-mech↗

arXiv2026

A covariant fermionic path integral for scalar Langevin processes with multiplicative white noise

We revisit the construction of the fermionic path-integral representation of overdamped scalar Langevin processes with multiplicative white noise, focusing on the covariance of the generating functional under non-linear changes of variables. We identify the transformations of the auxiliary (commuting and anticommuting) variables that ensure covariance under such transformations. The subtleties induced by the non-differentiable trajectories of the stochastic dynamics are encoded in the fermionic statistics. Upon integrating out the auxiliary variables, we derive the Onsager-Machlup formulation, which agrees with the one recently obtained using a higher-order discretization scheme. In contrast to the latter, the construction proposed here is formulated directly in continuous time.

cond-mat.stat-mech↗

arXiv2026

Universal Coarsening and Giant-Cluster Formation in Growing Interfaces

Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood. Here, we numerically investigate this unexplored coarsening of clusters in 2D growing interfaces believed to belong to the Kardar-Parisi-Zhang universality class. Using a two-point spatial correlator, we demonstrate statistical time invariance of the evolving configurations and identify scaling forms shared across distinct models. We reveal a pronounced asymmetry in the growth of the largest clusters: one cluster emerges as a giant structure whose characteristic length exceeds the correlation length. Population-dependent scaling forms for the number densities of cluster areas are uncovered. These findings highlight new universal aspects of growing interfaces and suggest avenues for experimental verification.

cond-mat.stat-mech↗

arXiv2026

The Wishart--Rosenzweig--Porter random matrix ensemble

In recent years the Rosenzweig--Porter (RP) ensemble, obtained by adding a diagonal matrix with independent and identically distributed elements to a Gaussian random matrix, has been widely used as a minimal model for the emergence of fractal eigenstates in complex many-body systems. A key open question concerns the robustness of its phase diagram when the assumption of independent and uncorrelated entries is relaxed -- an assumption that simplifies its analysis, but is generally violated in realistic quantum systems. In this work, we take a first step in this direction by considering a deformed Wishart (rather than Gaussian) random matrix, which we dub the ``Wishart--RP'' ensemble. Using perturbation theory, as well as the cavity and replica methods and the Dyson Brownian motion approach, we characterize its phase diagram and localization properties. Remarkably, we show that the level compressibility, which quantifies spectral correlations in the fractal phase, coincides with that of the Gaussian RP model, thereby extending the universality conjectured in [SciPost Phys. 14, 110 (2023)] beyond the fully uncorrelated setting. We confirm our results with numerical tests.

cond-mat.stat-mech↗

arXiv2025

Testing the Localization Landscape Theory on the Bethe Lattice

The Localization Landscape Theory (LLT) provides a classical picture of Anderson localization by introducing an effective confining potential whose percolation is proposed to coincide with the mobility edge. Although this proposal shows remarkable numerical agreement in three dimensions, its fundamental validity remains unsettled. Here we test the LLT analytically on the Bethe lattice, where both the Anderson localization transition and the LLT percolation problem are exactly solvable. We find that the two transitions do not coincide, and their critical behaviors differ markedly. In particular, LLT percolation displays standard mean-field percolation criticality that is fundamentally distinct from the peculiar critical behavior of the Anderson transition on the Bethe lattice. Our results provide an exact benchmark showing that, while geometrically intuitive, the LLT does not capture the true quantum critical properties of localization.

cond-mat.dis-nn↗

arXiv2025

Phase Separation Kinetics in a Polar Active Field Model

A milestone of phase separation kinetics is the emergence of universal power laws $\sim t^{1/z}$ governing the domain growth evolution. We investigate a phase-separating polar active model comprising a scalar density field with an advective coupling to a polarization field. Our analysis reveals a novel $\sim t^{0.6}$ regime, which agrees well with the accelerated growth recently observed in simulations of polar active particles. We provide analytical arguments to explain how advection facilitates the creation of topological defects and compresses the domains leading to faster growth. We also show that the $\sim t^{0.6}$ regime is robust to several model generalizations.

cond-mat.soft↗

arXiv2025

The geometric phase transition of the three-dimensional $\mathbb{Z}_2$ lattice gauge model

After fifty years of lattice gauge theories (LGTs), the nature of the transition between their topological phases (confinement/deconfinement) remains challenging due to the absence of a local order parameter. In this work, we conduct a percolation analysis of Wegner's three-dimensional $\mathbb{Z}_2$ lattice gauge model using intensive Monte Carlo simulations and finite-size scaling, offering fresh insights into the topological phase transitions of gauge-invariant systems. We demonstrate that, regardless of the connection rules, geometrical loops, constructed by piercing excited plaquettes percolate precisely at the thermal critical point $T_{\rm c}$, with critical exponents coinciding with those of the loop representation of the dual 3D Ising model. Further, we construct Fortuin-Kasteleyn (FK) clusters in a random-cluster representation, showing that they also percolate at $T_{\rm c}$, enabling access to all thermal critical exponents. Strikingly, the Binder cumulants of the percolation order parameters for both loops and FK clusters reveal a pseudo-first-order transition. This work sheds new light on the critical behavior of pure LGTs, with potential implications for condensed matter systems and quantum error correction.

cond-mat.stat-mech↗

arXiv2025

Introduction to Langevin Stochastic Processes

These lecture notes provide an introduction to Langevin processes and briefly discuss some interesting properties and simple applications. They compile material presented at the "School of Physics and Mathematics Without Frontiers" (ZigZag), held at La Havana, Cuba, in March 2024, the School "Information, Noise and Physics of Life" held at Niš, Serbia, in June 2024, both sponsored by ICTP, the PEBBLE summer camp at Westlake University, China, in August 2024, the Barcelona school on "Non-equilibrium Statistical Physics", in April 2025, and the 2012-2016 course "Out of Equilibrium Dynamics of Complex Systems" for the Master 2 program "Physics of Complex Systems" in the Paris area.

cond-mat.stat-mech↗

arXiv2024

Finite-frequency prethermalization in periodically driven ergodic systems

We investigate the periodically driven dynamics of many-body systems, either classical or quantum, finite-dimensional or mean-field, displaying an unbounded phase-space. Using the lattice $ϕ^4$ model and the $p$-spin spherical model as representative examples, we find that the inclusion of a smooth periodic drive atop an otherwise ergodic dynamics leads to a long-lived prethermalization, even at moderate driving frequencies. In specific asymptotic limits, we compute the corresponding prethermal Hamiltonian from an analytical perturbation scheme.

cond-mat.stat-mech↗

arXiv2024

Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs

We study the spectral properties of the adjacency matrix in the giant connected component of Erdös-Rényi random graphs, with average connectivity $p$ and randomly distributed hopping amplitudes. By solving the self-consistent cavity equations satisfied by the matrix elements of the resolvent, we compute the probability distribution of the local density of states, which governs the scaling with the system size of the moments of the eigenvectors' amplitudes, as well as several other observables related to the spectral statistics. For small values of $p>1$ above the percolation threshold, we unveil the presence of an exotic delocalized but (weakly) multifractal phase in a broad region of the parameter space, which separates the localized phase found for $p\le1$ from the fully-delocalized GOE-like phase expected for $p\to \infty$. We explore the fundamental physical mechanism underlying the emergence of delocalized multifractal states, rooted in the pronounced heterogeneity in the topology of the graph. This heterogeneity arises from the interplay between strong fluctuations in local degrees and hopping amplitudes, and leads to an effective fragmentation of the graph. We further support our findings by characterizing the level statistics and the two-point spatial correlations within the multifractal phase, and address the ensuing anomalous transport and relaxation properties affecting the quantum dynamical evolution.

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