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

TL;DR

This paper investigates nonrandomly frustrated Ising models and demonstrates through simulations that they exhibit logarithmically slow domain growth due to barriers proportional to domain size, challenging the expectation of faster growth in non-random systems.

Contribution

The study provides the first evidence of logarithmic domain growth in nonrandomly frustrated systems, supported by physical arguments and Monte Carlo simulations.

Findings

Barriers to domain growth grow proportionally with domain size.

Logarithmic slow dynamics observed in simulations.

Systems order more quickly when cooled gradually rather than quenched.

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).