相关论文: Dilution Robustness for Mean Field Ferromagnets

We study the mean field dilute model of a ferromagnet. We find and prove an expression for the free energy density at high temperature, and at temperature zero. We find the critical line of the model, separating the phase with zero…

The question of robustness of a network under random ``attacks'' is treated in the framework of critical phenomena. The persistence of spontaneous magnetization of a ferromagnetic system to the random inclusion of antiferromagnetic…

We studied nonsparsely diluted mean-field models that differ from sparsely diluted mean-field models, such as the Viana--Bray model. When the existence probability of each edge follows a Bernoulli distribution, we rigorously prove that the…

Deep neural networks have achieved impressive performance on a variety of tasks, but their brittleness to distributional shifts remains a significant barrier to real-world deployment. In this paper, we propose a framework to analyse and…

We consider the complexity of random ferromagnetic landscapes on the hypercube $\{\pm 1\}^N$ given by Ising models on the complete graph with i.i.d. non-negative edge-weights. This includes, in particular, the case of Bernoulli disorder…

We study the predictability of zero-temperature Glauber dynamics in various models of disordered ferromagnets. This is analyzed using two independent dynamical realizations with the same random initialization (called twins). We derive,…

We conpare predictions of the mean-field theory of supercnductivity for metallic systems on the border of a density instability for cubic and tetragonal lattices. The calculations are based on a parametrisation of an effective interaction…

We calculate magnetic couplings in the $J_{pd}$ model for dilute magnets, in order both to identify the relevant parameters which control ferromagnetism and also to bridge the gap between first principle calculations and model approaches.…

In this paper we compute exactly the ground state energy and entropy of the dilute ferromagnetic Ising model. The two thermodynamic quantities are also computed when a magnetic field with random locations is present. The result is reached…

Two models of loss networks, introduced by Gibbens et al. and by Antunes et al., are known to exhibit a mean field limiting regime with several stable equilibria. These models are reexamined in the light of Freidlin and Wentzell's large…

We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…

We reveal large fluctuations in the response of real multiplex networks to random damage of nodes. These results indicate that the average response to random damage, traditionally considered in mean-field approaches to percolation, is a…

Using Brownian dynamics simulations we study gel-forming colloid-polymer mixtures. The focus of this article lies on the differences of dense and dilute gel networks in terms of structure formation both on a local and a global level. We…

We report an observation of a stable soliton-like structure on the surface of a ferrofluid, generated by a local perturbation in the hysteretic regime of the Rosensweig instability. Unlike other pattern-forming systems with localized 2D…

A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a three-dimensional variational…

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent…

Counterion distributions at charged soft membranes are studied using perturbative analytical and simulation methods in both weak coupling (mean-field or Poisson-Boltzmann) and strong coupling limits. The softer the membrane, the more…

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…

Ferrofluids are strongly paramagnetic liquids. We study the behavior of ferrofluid droplets confined between two parallel plates with a weak applied field parallel to the plates. The droplets elongate under the applied field to reduce their…

The dual-fermion approach offers a way to perform diagrammatic expansion around the dynamical mean-field theory. Using this formalism, the influence of antiferromagnetic fluctuations on the self-energy is taken into account through…