Optimization and inference in machine learning and physics Workshop

Replica symmetry breaking in the `small world' spin glass

author: Bastian Wemmenhove, Radboud University Nijmegen

Description

We apply the cavity method to an Ising spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. Using the scheme developed by Mézard & Parisi for the Bethe lattice, we evaluate observables for a model with fixed connectivity and +/- J long range bonds. Furthermore, we determine the stability of the RS solution by making an ansatz on the form of the functional 1RSB order parameters.

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*Slides*
0:01	1RSB in the ‘small-world’ spin glass
2:08	Introduction and motivation
3:54	Why bother?
10:09	Definitions
13:07	Dealing with the randomness
16:44	The Cavity method on a random graph
28:09	The Cavity method on a random graph (cont.)
30:02	Cavity method for the ‘small-world’ lattice
40:37	Cavity method for the ‘small-world’ lattice (cont.)
40:46	One step RSB
46:07	One step RSB (cont.)
53:19	Numerical results
56:25	Numerical results (cont.)
57:48	Simulations
59:05	Conclusions and outlook

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