Effect of Disorder in the Frustrated Ising FCC Antiferromagnet: Phase Diagram and Stretched Exponential Relaxation

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 \(p\sim 0.01\), in agreement with theories and simulations on other 3D models. The antiferromagnetic long-range order is also destroyed with a very small \(p\) (\(\simeq 5%\)). 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 (\(T_c,p\)) shows an asymmetry, unlike the case of the \(\pm J\) 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 \(\simeq 1/3\) 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.