# Criticality in diluted ferromagnets

@article{Agliari2008CriticalityID, title={Criticality in diluted ferromagnets}, author={Elena Agliari and Adriano Barra and Federico Camboni}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2008}, volume={2008}, pages={P10003} }

We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet using analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non-trivial phase by commutativity breaking of the infinite volume limit…

## 23 Citations

ON FERROMAGNETIC DILUTED p-SPIN MODEL

- Physics
- 2010

In this paper we develop the interpolating cavity field technique for the mean field ferromagnetic p-spin. The model we introduce is a natural extension of the diluted Curie–Weiss model to p > 2 spin…

Dilution robustness for mean field ferromagnets

- Mathematics, Physics
- 2009

In this work we compare two different random dilutions on a mean field ferromagnet: the first model is built on a Bernoulli diluted graph while the second lives on a Poisson diluted one. While it is…

A two-populations Ising model on diluted random graphs

- Physics
- 2010

We consider the Ising model for two interacting groups of spins embedded in an Erdös–Rényi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo…

Spin Glass Identities and the Nishimori Line

- Mathematics
- 2008

For a general spin glass model with asymmetric couplings we prove a family of identities involving expectations of generalized overlaps and magnetizations in the quenched state. Those identities hold…

Dilution of Ferromagnets via a Random Graph-Based Strategy

- Computer ScienceComplex.
- 2018

This work proposes a Monte Carlo method, based on random graphs, for modeling ferromagnets with dimension D≥4, which can be approximated by the Curie-Weiss model, and uses a modified version of the Erdős-Renyi graph model for this purpose.

Notes on the p-spin glass studied via Hamilton-Jacobi and smooth-cavity techniques

- Physics
- 2012

In these notes, we continue our investigation of classical toy models of disordered statisticalmechanics, through techniques recently developed and testedmainly on the paradigmatic…

Mean-field cooperativity in chemical kinetics

- PhysicsTheoretical Chemistry Accounts
- 2012

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and…

On quantum and relativistic mechanical analogues in mean-field spin models

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

Conceptual analogies among statistical mechanics and classical or quantum mechanics have often appeared in the literature. For classical two-body mean-field models, such an analogy is based on the…

Analogue neural networks on correlated random graphs

- Physics
- 2012

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…

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