We study the problem of disorder chaos in the spherical mean-field model. It concerns the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra’s replica symmetry breaking scheme, we establish this at the levels of the free energy and the Gibbs measure.
Bibliographical noteFunding Information:
The authors thank D. Feehan, M. Slatkin, and P. Wilton for discussions about death rate estimation, and R. Durbin, C. Freeman, and G. McVean for discussions about UK Biobank markers. This work is supported by US National Institutes of Health (NIH) grant R01GM116044 to R.N.
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- Disorder chaos
- Mean-field model
- Replica symmetry breaking