Phase transitions in atypical systems induced by a condensation transition on graphs
arXiv:1909.10564 · doi:10.1103/PhysRevE.101.012133
Abstract
Random graphs undergo structural phase transitions that are crucial for dynamical processes and cooperative behavior of models defined on graphs. In this work we investigate the impact of a first-order structural transition on the thermodynamics of the Ising model defined on Erdös-Rényi random graphs, as well as on the eigenvalue distribution of the adjacency matrix of the same graphical model. The structural transition in question yields graph samples exhibiting condensation, characterized by a large number of nodes having degrees in a narrow interval. We show that this condensation transition induces distinct thermodynamic first-order transitions between the paramagnetic and the ferromagnetic phases of the Ising model. The condensation transition also leads to an abrupt change in the global eigenvalue statistics of the adjacency matrix, which renders the second moment of the eigenvalue distribution discontinuous. As a side result, we derive the critical line determining the percolation transition in Erdös-Rényi graph samples that feature condensation of degrees.
arXiv comment11 pages, 4 figures
References in corpus (44)
- Error and attack tolerance of complex networks
- Epidemic spreading in scale-free networks
- Network robustness and fragility: Percolation on random graphs
- Critical phenomena in complex networks
- Breakdown of the Internet under intentional attack
- Connectivity of Growing Random Networks
- The Bethe lattice spin glass revisited
- Bose-Einstein condensation in complex networks
- The statistical mechanics of networks
- Ising Model on Networks with an Arbitrary Distribution of Connections
- Ferromagnetic ordering in graphs with arbitrary degree distribution
- Frequency synchronization in random oscillator network
- Solution of the 2-star model of a network
- Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
- Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses
- Scaling theory of the Anderson transition in random graphs: ergodicity and universality
- Spectra of Sparse Random Matrices
- Synchronization transition in scale-free networks: Clusters of synchrony
- Random incidence matrices: moments of the spectral density
- Network Transitivity and Matrix Models
- On the localization transition in symmetric random matrices
- Statistical mechanics of topological phase transitions in networks
- Parallel dynamics of disordered Ising spin systems on finitely connected random graphs
- Rare events and discontinuous percolation transitions
- Eigenvalue tunnelling and decay of quenched random networks
- Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
- Distribution of diameters for Erdös-Rényi random graphs
- Finitely connected vector spin systems with random matrix interactions
- Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure
- Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
- Localization of eigenvectors in random graphs
- Condensation of Fluctuations in and out of Equilibrium
- Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices
- Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs
- Perturbing General Uncorrelated Networks
- Organization of complex networks without multiple connections
- The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
- Large deviation theory for diluted Wishart random matrices
- The two-star model: exact solution in the sparse regime and condensation transition
- Probability distributions with singularities
- Condensation of degrees emerging through a first-order phase transition in classical random graphs
- Imaginary replica analysis of loopy regular random graphs
- Theory for the conditioned spectral density of non-invariant random matrices
- Finite-size effects in exponential random graphs and cluster evaporation