Critical properties of a three-dimensional spherical model with random spin layers

A ferromagnetic system with frozen-in defects is investigated within a modified spherical model: The three-dimensional lattice is formed out of homogeneous layers which are occupied at random either by $A$ or by $B$ spins. We assume three exchange constants $J_A$, $J_B$, $J_{\mathrm{AB}}$ which correspond to the coupling between $A-A$, $B-B$, and $A-B$ spins, respectively. Moreover, two types of layer configurations are considered. (i) The first one allows for the occurrence of arbitrarily large clusters of connected layers which contain the same spins only; (ii) in the second type, homogeneous clusters larger than a certain size are excluded. In case (ii) the randomness of the layer distribution prohibits long-range order in the following sense: If we add one layer to a finite lattice of thickness $d$, then its influence on the free energy decreases exponentially with $d$; this theorem is proved to be true for all temperatures and any particular layer configuration. We then specialize to $J_{\mathrm{AB}}=0\mathrm{}$. In case (i) we find a finite critical temperature $T_c$ which is indicated by a molecular-field-like jump in the specific heat. This singularity turns out to belong to the class of Griffiths singularities. The surprising fact that we have here a "visible" Griffiths singularity is attributed to fluctuations in the spin length. In case (ii) no critical behavior is observed.