Criticality in diluted ferromagnet

Abstract

We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet by 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 and a suitable vanishing field. We find full agreement among theory, simulations and previous results.

23 pages, 3 figures

References in corpus (17)

• Statistical mechanics of complex networks
• General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
• On the Stability of the Quenched State in Mean Field Spin Glass Models
• About the overlap distribution in mean field spin glass models
• Spin-Glass Stochastic Stability: a Rigorous Proof
• The mean field Ising model trough interpolating techniques
• The infinite volume limit in generalized mean field disordered models
• Irreducible free energy expansion and overlaps locking in mean field spin glasses
• Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
• Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices
• Mean field dilute ferromagnet I. High temperature and zero temperature behavior
• Stochastic Stability
• Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
• Bipartite Mean Field Spin Systems. Existence and Solution
• Positive-Overlap Transition and Critical Exponents in Mean Field Spin Glasses
• Thermodynamic Limit for Mean-Field Spin Models
• Spin Glass Identities and the Nishimori Line

Cited by in corpus (18)

• A Hebbian approach to complex network generation
• Hierarchical neural networks perform both serial and parallel processing
• A statistical mechanics approach to autopoietic immune networks
• Parallel processing in immune networks
• Notes on the p-spin glass studied via Hamilton-Jacobi and Smooth-Cavity techniques
• Phase transition for the Maki-Thompson rumour model on a small-world network
• Mean-field cooperativity in chemical kinetics
• Equilibrium statistical mechanics on correlated random graphs
• Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution
• A Two-populations Ising model on diluted Random Graphs
• Analogue neural networks on correlated random graphs
• A walk in the statistical mechanical formulation of neural networks
• Dilution Robustness for Mean Field Ferromagnets
• Notes on ferromagnetic diluted P-spin model
• Collective behaviours: from biochemical kinetics to electronic circuits
• Single-Nodal Spontaneous Symmetry Breaking in NLP Models
• Dilution of Ferromagnets via a Random Graph-based Strategy
• A numerical investigation of the jamming transition in traffic flow on diluted planar networks