No-passing Rule in the Ground State Evolution of the Random-Field Ising Model

Abstract

We exactly prove the no-passing rule in the ground state evolution of the random-field Ising model (RFIM) with monotonically varying external field. In particular, we show that the application of the no-passing rule can speed up the calculation of the zero-temperature equilibrium $M(H)$ curve dramatically.

7 pages, 4 figures

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• Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems
• Critical behavior of the random-field Ising model with long-range interactions in one dimension
• Dimensional reduction and its breakdown in the 3-dimensional long-range random field Ising model
• Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems
• Random field Ising model : statistical properties of low-energy excitations and of equilibrium avalanches
• Critical Exponents of the Random Field Hierarchical Model
• Low-energy excitations in the three-dimensional random-field Ising model
• An improved Belief Propagation algorithm finds many Bethe states in the random field Ising model on random graphs
• Effect of disorder on condensation in the lattice gas model on a random graph
• On the breakdown of dimensional reduction and supersymmetry in random-field models