Remanence effects for spin glasses with sequential dynamics: exact results

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Abstract
The remanent magnetization and the remanent energy are calculated exactly for the +or-J spin glass in one dimension with random field and on Cayley trees for sequential dynamics at zero temperature. The method used is an iteration scheme which classifies different kinds of spins. In one dimension a value of 11/60 is found for the remanent magnetization. As expected, the result for the Cayley tree strongly depends on the boundary conditions. The tree with branching number 2 at its 'equilibrium' (i.e. the distribution of the boundary is the same as for the bulk) has a remanent magnetization of 1/7 (-33+25 square root 2) approximately=0.336.