Persistence in systems with algebraic interaction

Persistence in coarsening one-dimensional spin systems with: a power-law in teraction r(-1-sigma) is considered. Numerical studies indicate that for su fficiently large values of-the interaction exponent sigma (sigma greater th an or equal to 1/2 in our simulations), persistence decays as an algebraic function of the length scale L, P(L) similar to L-theta. The persistence ex ponent a is found to be independent on the force exponent sigma and close t o its value for the extremal (sigma -->infinity) model, <(theta)over bar>=0 .175 075 88.... For smaller values of the ford: exponent (sigma<1/2), finit e size effects prevent the system from reaching the asymptotic regime. Scal ing arguments suggest that in order to avoid significant boundary effects f or small sigma, the system size should grow as [O(1/sigma)](1/sigma). [S106 3-651X(99)51009-X].