  In this paper, we consider limit laws for the model, which is a
generalisation of the random energy model (REM) to the case when the energy
levels have the mixture distribution. More precisely, the distribution of the
energy levels is assumed to be a mixture of two normal distributions, one of
which is standard normal, while the second has the mean \(\sqrt{n}a\) with some
\(a\in \R,\) and the variance \(\sigma \ne 1\). The phase space \((a,\sigma)
\subset \R \times \R_+\) is divided onto several domains, where after
appropriate normalisation, the partition function converges in law to the
stable distribution. These domains are separated by the critical surfaces,
corresponding to transitions from the normal distribution to \(\alpha-\)stable
with \(\alpha \in (1,2)\), after to 1-stable, and finally to \(\alpha-\)stable
with \(\alpha \in (0,1).\) The corresponding phase diagram is the central
result of this paper.
