Large Deviations of Correlation Functions in Random Magnets

Abstract

We present a large deviations theory of the spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, both at finite and zero temperature. Rare events of atypically correlated variables are particularly important at the critical point: the phase transition is driven by few pairs of strongly correlated spins, while the majority remains basically uncorrelated. At the zero temperature critical point the number of spin pairs correlated over a distance L is shown to be no longer exponential, but only linear in the spins separation.

19 pages, 9 figures

References in corpus (5)

• The large deviation approach to statistical mechanics
• Loop series for discrete statistical models on graphs
• Diluted Mean-Field Spin-Glass Models at Criticality
• Random-field p-spin glass model on regular random graphs
• Finite size scaling of the de Almeida-Thouless instability in random sparse networks

Cited by in corpus (14)

• Two critical localization lengths in the Anderson transition on random graphs
• Approximating the XY model on a random graph with a $q$-state clock model
• The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism
• The marginally stable Bethe lattice spin glass revisited
• Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
• New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs
• One-dimensional disordered Ising models by replica and cavity methods
• Soft modes in jammed hard spheres (I): Mean field theory of the isostatic transition
• Ising spin glass in a random network with a gaussian random field
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• Large Deviations of the Finite-Time Magnetization of the Curie-Weiss Random Field Ising Model