Griffiths phase in a three-dimensional Ising model with aperiodic interactions.

Abstract

We simulate a ferromagnetic Ising model with aperiodic interactions in three dimensions using the Monte Carlo method. When the strength of aperiodicity is weak, the systems exhibit behavior similar to that of a pure system. As we increase the value of r, we observe that the heat capacity develops a multipeak structure for all sequences. For both marginal and relevant sequences, we observe a region of divergent susceptibility, indicating the existence of a Griffiths phase. We find that the extent of this region is related to the wandering exponent and the strength of aperiodicity.