Modified TAP equations for the SK spin glass

Modified TAP equations for the SK spin glass

The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. The natural requirement of self-consistency leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results be...

Spreading of Damage in the SK Spherical Spin Glass

By considering the Langevin dynamics of the SK spin glass with a spherical constraint we calculate the asymptotic distance between two real replicas that evolve with the same thermal noise from different initial conditions. Despite the simplicity of the model its dynamics is known to be non trivial and presents aging phenomena. We found that the asympotic distance between two replicas is maxima...

Dyson’s equations for the (Ising) spin-glass

A complex problem is solved herej we show how to write Dyson's equations for trie (Ising) spin-glass that relate the propagator G ta trie mass operator M. In other words we are able to reduce trie inversion of an ultrametric matrix M to the solution of a Dyson's equation in ail sectors (for the replicon sectcr trie result had already been derived). It turns oui that what renders the problem tra...

Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition

An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This corresponds to the approach made by Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin glasses. Taking into account the fact that in the Hopfield model there exist correlations between d...

A Simple hypothesis for the spin glass phase of the pnfinite-ranged SK model