Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions

Abstract

It is known that in systems which contain randomness explicitly in their Hamiltonians (e.g., due to impurities), the characteristic size L of the ordered domains can grow only logarithmically with time t following a quench below the transition temperature. However, in systems without such imposed randomness, much faster power law growth has generally been predicted. Motivated by the slow dynamics present in glasses, we have been looking for counterexamples, i.e., for models without randomness which nonetheless order logarithmically slowly. Here, we discuss two closely related models for which we have simple physical arguments that such slow growth occurs. The basis of these arguments is the claim that the free energy barriers to domain growth in these models are proportional to L. Thus, the barriers grow as the domains coarsen. We present the results of Monte Carlo simulations, which lend strong support to our claims of growing barriers and logarithmically slow dynamics. Finally, we discuss how quickly the system orders when it is cooled continuously through the transition (rather than quenched).