Disorder chaos in some diluted spin glass models

Abstract

We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: $K$-spin antiferromagnetic Ising model for even $K\ge 2$, $K$-spin spin glass model for even $K\ge 2$, and random $K$-sat model for all $K\ge 2$. We show that modifying even a small proportion of clauses results in near maximizers of the original and modified Hamiltonians being nearly orthogonal to each other with high probability. We use a standard technique of approximating diluted models by appropriate fully connected models and then apply disorder chaos results in this setting, which include both previously known results as well as new examples motivated by the random $K$-sat model.

References in corpus (5)

• Chaos, concentration, and multiple valleys
• A connection between MAX $\kappa$-CUT and the inhomogeneous Potts spin glass in the large degree limit
• Optimization on Sparse Random Hypergraphs and Spin Glasses
• Parisi formula for the ground state energy in the mixed p-spin model
• On the $K$-sat model with large number of clauses

Cited by in corpus (1)

• On the $K$-sat model with large number of clauses