arXiv subjects

Valentin Anfray

Publications and source records attributed to Valentin Anfray.

5 recordsLinked to original sources

arXiv2026

Diffusion disorder in the contact process

We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a spatially uniform diffusion term. Correspondingly, we find quenched randomness in the diffusion rates to be irrelevant by power counting in the field-theory of the contact process. However, large-scale Monte Carlo simulations demonstrate that such diffusion disorder destabilizes the clean directed percolation critical point. Instead, the transition belongs to the same infinite-randomness universality class as the contact process with disorder in the infection or healing rates. To explain these results, we develop an effective model with an infinite diffusion rate; it shows that diffusion disorder generates an effective disorder in the healing rates. The same mechanism also appears in the field-theoretic description: Whereas diffusion disorder is irrelevant by power-counting, it generates standard random-mass disorder under renormalization. We discuss the validity of this mechanism for other absorbing state transitions and non-equilibrium phase transitions in general.

cond-mat.stat-mech↗

arXiv2025

Diffusive Epidemic Process with quenched disorder

Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model whose absorbing-state transition is controlled by the relative diffusion of healthy and infected species, provides a natural setting for this question. Using a new single-seed algorithm that effectively simulate infinite systems for the infected individuals, we find that effective global diffusion rates can be used to predict disorder relevance and we identify two distinct infinite-disorder fixed points. Notably, we find that disorder in diffusion rates is qualitatively different from that in reaction rates as it can even induce a total suppression of the active phase, a phenomenon not observed with other types of disorder. These results establish mobility disorder as a distinct route by which quenched heterogeneity qualitatively reorganizes spreading dynamics, with implications for systems ranging from cell polarity to epidemic propagation in heterogeneous media.

cond-mat.stat-mech↗

arXiv2023

Non-monotonic flow variations in a TASEP-based traffic model featuring cars searching for parking

The Totally Asymmetric Simple Exclusion Process (TASEP) is a paradigm of out-of-equilibrium Statistical Physics that serves as a simplistic model for one-way vehicular traffic. Since traffic is perturbed by cars cruising for parking in many metropolises, we introduce a variant of TASEP, dubbed SFP, in which particles are initially cruising at a slower speed and aiming to park on one of the sites adjacent to the main road, described by a unidimensional lattice. After parking, they pull out at a finite rate and move at a normal speed. We show that this model, which breaks many of the conservation rules applicable in other TASEP variants, exhibits singular features, in particular non-monotonic variations of the steady-state current with the injection rate and re-entrant transitions in the phase diagram, for some range of parameters. These features are robust to variations in the update rule and the boundary conditions.Neither the slow speed of cruising cars nor the perturbation of the flow due to pull-out maneuvers, taken in isolation, can rationalize these observations. Instead, they originate in a cramming (or `paper jam') effect which results from the coupling of these mechanisms: injecting too many cars into the system saturates the first sites of the road, which prevents parked cars from pulling out, thus forcing cruising cars to travel farther along the road.These strong discrepancies with even the qualitative trends of the baseline TASEP model highlight the importance of considering the effect of perturbations on traffic.

cond-mat.stat-mech↗

arXiv2022

Numerical evidences of a universal critical behavior of 2D and 3D random quantum clock and Potts models

The random quantum $q$-state clock and Potts models are studied in 2 and 3 dimensions. The existence of Griffiths phases is tested in the 2D case with $q=6$ by sampling the integrated probability distribution of local susceptibilities of the equivalent McCoy-Wu 3D classical modelswith Monte Carlo simulations. No Griffiths phase is found for the clock model. In contrast, numerical evidences of the existence of Griffiths phases in the random Potts model are given and the Finite Size effects are analyzed. The critical point of the random quantum clock model is then studied by Strong-Disorder Renormalization Group. Despite a chaotic behavior of the Renormalization-Group flow at weak disorder, evidences are given that this critical behavior is governed by the same Infinite-Disorder Fixed Point as the Potts model, independently from the number of states $q$.

cond-mat.dis-nn↗

arXiv2021

Numerical evidence of a super-universality of the 2D and 3D random quantum Potts models

The random q-state quantum Potts model is studied on hypercubic lattices in dimensions 2 and 3 using the numerical implementation of the Strong Disorder Renormalization Group introduced by Kovacs and Igl{\'o}i [Phys. Rev. B 82, 054437 (2010)]. Critical exponents $\nu$, d f and $\psi$ at the Infinite Disorder Fixed Point are estimated by Finite-Size Scaling for several numbers of states q between 2 and 50. When scaling corrections are not taken into account, the estimates of both d f and $\psi$ systematically increase with q. It is shown however that q-dependent scaling corrections are present and that the exponents are compatible within error bars, or close to each other, when these corrections are taking into account. This provides evidence of the existence of a super-universality of all 2D and 3D random Potts models.

cond-mat.dis-nn↗