  We propose a plasma model for spectral statistics displaying level repulsion
without long-range spectral rigidity, i.e. statistics intermediate between
random matrix and Poisson statistics similar to the ones found numerically at
the critical point of the Anderson metal-insulator transition in disordered
systems and in certain dynamical systems. The model emerges from Dysons
one-dimensional gas corresponding to the eigenvalue distribution of the
classical random matrix ensembles by restricting the logarithmic pair
interaction to a finite number $k$ of nearest neighbors. We calculate
analytically the spacing distributions and the two-level statistics. In
particular we show that the number variance has the asymptotic form
$\Sigma^2(L)\sim\chi L$ for large $L$ and the nearest-neighbor distribution
decreases exponentially when $s\to \infty$, $P(s)\sim\exp (-\Lambda s)$ with
$\Lambda=1/\chi=k\beta+1$, where $\beta$ is the inverse temperature of the gas
($\beta=$1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class
respectively). In the simplest case of $k=\beta=1$, the model leads to the
so-called Semi-Poisson statistics characterized by particular simple
correlation functions e.g. $P(s)=4s\exp(-2s)$. Furthermore we investigate the
spectral statistics of several pseudointegrable quantum billiards numerically
and compare them to the Semi-Poisson statistics.
