Effect of disorder in the frustrated Ising FCC antiferromagnet: phase diagram and stretched exponential relaxation

Abstract

In this paper, we study the phase transition in a face-centered-cubic antiferromagnet with Ising spins as a function of the concentration p of ferromagnetic bonds randomly introduced into the system. Such a model describes the spin-glass phase at strong bond disorder. Using the standard Monte Carlo simulation and the powerful Wang–Landau flat-histogram method, we carry out in this work intensive simulations over the whole range of p. We show that the first-order transition disappears with a tiny amount of ferromagnetic bonds, namely p ~ 0.01, in agreement with theories and simulations on other 3D models. The antiferromagnetic long-range order is also destroyed with a very small p (≃5%). With increasing p, the system changes into a spin glass and then to a ferromagnetic phase when p > 0.65. The phase diagram in the space (Tc, p) shows an asymmetry, unlike the case of the ±J Ising spin glass on the simple cubic lattice. We calculate the relaxation time around the spin-glass transition temperature and we show that the spin autocorrelation follows a stretched exponential relaxation law where the factor b is equal to ≃1/3 at the transition as suggested by the percolation-based theory. This value is in agreement with experiments performed on various spin glasses and with Monte Carlo simulations on different SG models.