arXiv subjects

Isaac Pérez Castillo

Publications and source records attributed to Isaac Pérez Castillo.

58 records · Page 4Linked to original sources

arXiv2009

Spectral density of random graphs with topological constraints

The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case an exact solution is found for the spectral density in the form of consistency equations depending on the statistical properties of the graph ensemble in question. We highlight the effect of these topological constraints on the resulting spectral density.

cond-mat.dis-nn↗

arXiv2008

Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices

The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a closed set of equations from which the density of eigenvalues can be efficiently calculated. Within this approach, the Wigner semicircle law for Gaussian matrices and the Marcenko-Pastur law for covariance matrices are recovered easily. Our results are compared with numerical diagonalization, finding excellent agreement.

cond-mat.dis-nn↗

arXiv2005

Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices

We study XY spin systems on small world lattices for a variety of graph structures, e.g. Poisson and scale-free, superimposed upon a one dimensional chain. In order to solve this model we extend the cavity method in the one pure-state approximation to deal with real-valued dynamical variables. We find that small-world architectures significantly enlarge the region in parameter space where synchronization occurs. We contrast the results of population dynamics performed on a truncated set of cavity fields with Monte Carlo simulations and find excellent agreement. Further, we investigate the appearance of replica symmetry breaking in the spin-glass phase by numerically analyzing the proliferation of pure states in the message passing equations.

cond-mat.dis-nn↗

arXiv2005

On exact mappings between fermionic Ising spin glass and classical spin glass models

We present in this paper exact analytical expressions for the thermodynamical properties and Green functions of a certain family of fermionic Ising spin-glass models with Hubbard interaction, by noticing that their Hamiltonian is a function of the number operator only. The thermodynamical properties are mapped to the classical Ghatak-Sherrington spin-glass model while the the Density of States (DoS) is related to its joint spin-field distribution. We discuss the presence of the pseudogap in the DoS with the help of this mapping.

cond-mat.dis-nn↗