Growth and equilibration in the two-dimensional random-field Ising model

Abstract

The nonequilibrium and equilibrium behavior of the two-dimensional Ising model are studied after rapid cooling in a random field. Extensive Monte Carlo simulations are presented, covering a wide range of temperature and random-field strength. Quantitative comparison is made with several recent theories of domain growth and equilibration. In particular, strong support is given to the Villain-Grinstein-Fernandez theory of logarithmic growth.

Near-Critical Fluctuations and Cytoskeleton-Assisted Phase Separation Lead to Subdiffusion in Cell Membranes

“…As is evident from the Figure, at the end of a simulation run of 6 × 10 6 MC cycles, the domain sizes are indeed R(t) ∼ R comp . Although some growth is still observed at this stage, it is so slow, that at present it is unclear, whether the system will evolve toward a disordered equilibrium state featuring a number of small domains, as suggested in [47,48], or the slow logarithmic growth will continue further to produce eventually (after an extremely long time) a single domain with the size R ∞ . What is clear, though, that the time required for complete : Figure 3: Effect of the membrane skeleton on the the domain growth in DMPC/DSPC 50:50 membrane abruptly cooled from the all-fluid state down to T = 310 K in the fluid-gel phase coexistence region.…”

Ordering dynamics in Disordered systems

“…A more detailed MC study of the d ¼ 2 RFIM with Glauber kinetics is due to Anderson (1987), who presented results for a range of quench temperatures and random-field amplitudes. Anderson focused on the growth law and undertook a careful test of the various theoretical predictions discussed in Section 2.4.…”

Dynamical properties of random-field Ising model

“…In most of the studies on RFIM, the domain size (or the cluster size) was determined in terms of the fluctuations of the magnetization [17][18][19][20][21]. The fluctuations in magnetization is only a measure of domain size, not the actual domain size.…”