One-dimensional disordered Ising models by replica and cavity methods

Abstract

Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor graph (p-spin) ensembles. We present exact analytical expressions, which can be efficiently approximated numerically, for many types of correlation functions and for the average free energies of open and closed finite chains. All the results achieved, with the exception of those involving closed chains, are then rigorously derived without replicas, using a probabilistic approach with the same flavour of cavity method.

References in corpus (3)

• Diluted Mean-Field Spin-Glass Models at Criticality
• Thermodynamics of the Lévy spin glass
• Large Deviations of Correlation Functions in Random Magnets

Cited by in corpus (5)

• Loop expansion around the Bethe approximation through the $M$-layer construction
• New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature
• One-loop diagrams in the Random Euclidean Matching Problem
• Random-link matching problems on random regular graphs
• Replica bound for Ising spin glass models in one dimension