Dynamic mean-field and cavity methods for diluted Ising systems

2011/09/30 by Erik Aurell, Hamed Mahmoudi · 37 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Field (mathematics) #Ising model #Markov Chains and Monte Carlo Methods #Mathematics #Physics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.85.031119

published in Physical Review E 85(3), 031119 (American Physical Society)

openalex publication_date 2012/03/16 · arxiv created 2012/03/20 · arxiv updated 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We compare dynamic mean-field and dynamic cavity methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and we compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks, the dynamic cavity method generally predicts magnetizations of individual spins better than both first-order ("naive") and second-order ("TAP") dynamic mean-field theory.

Citations

• Solution of 'Solvable model of a spin glass'
• Onsager's reaction field for the Potts model from the path integral
• Dynamical TAP equations for non-equilibrium Ising spin glasses
• An Exactly Solvable Asymmetric Neural Network Model
• Fluctuation–dissipation: Response theory in statistical physics
• Stochastic Processes in Physics and Chemistry

Cited by

• Path integral methods for the dynamics of stochastic and disordered systems