A mean-field free-energy surface of a dilute Ising antiferromagnet on two-, three-, and four-dimensional lattices is studied numerically as a function of temperature and an applied magnetic field. In the presence of the field parallel to spins, the dilute Ising antiferromagnet is believed to map onto the random-field Ising model providing a convenient experimental realization. From the hysteretic behavior we identify three temperature regions: (1) a high-temperature equilibrium region above the hysteresis boundary $T_H$ where an accessed state is independent of the sample history; (2) a low-temperature region below $T_c$ where the antiferromagnetic state has the lowest free energy; (3) an intermediate-temperature region $T_c<T<\mathrm{}{T}_H$ where the accessed state depends on the sample history, but the domain state has a lower free energy than the antiferromagnetic state. When the sample is cooled in a finite field, the domains are formed and stabilized below $T_H$. Thus the antiferromagnetic state is inaccessible in our simulation. In contrast, once the antiferromagnetic order is prepared at low temperatures and the temperature is raised in the finite field, the sample remains in the antiferromagnetic state until $T_c$ and then the domains nucleate above $T_c$, and finally the sample recovers the high-temperature equilibrium state at $T_H$. In recent neutron scattering experiments on three-dimensional (3D) Ising antiferromagnets, the analogous behavior is observed. Using the simulation results, we argue that strong domain-wall pinning prevents long-range order from occurring in 3D samples when cooled with $H\ne 0$, despite the theoretical consensus that the lower critical dimension in equilibrium is 2 for the random-field Ising model.

• Received 24 February 1984

DOI:https://doi.org/10.1103/PhysRevB.30.5220