  We study the limiting spectral distribution of sample covariance matrices
$XX^T$, where $X$ are $p\times n$ random matrices with correlated entries, for
the cases $p/n\to y\in [0,\infty)$. If $y>0$, we obtain the Mar\v{c}enko-Pastur
distribution and in the case $y=0$ the semicircle distribution (after
appropriate rescaling). The entries we consider are Curie-Weiss spins, which
are correlated random signs, where the degree of the correlation is governed by
an inverse temperature $\beta>0$. The model exhibits a phase transition at
$\beta=1$. The correlation between any two entries decays at a rate of $O(np)$
for $\beta \in (0,1)$, $O(\sqrt{np}$) for $\beta=1$, and for $\beta>1$ the
correlation does not vanish in the limit. In our proofs we use Stieltjes
transforms and concentration of random quadratic forms.
