  Matrix models have been shown to be equivalent to noncommutative field
theories. In this work we study noncommutative X-Y model and try to understand
Kosterlitz Thouless transition in it by analysing the equivalent matrix model.
We consider the cases of a finite lattice and infinite lattice separately. We
show that the critical value of the matrix model coupling is identical for the
finite and infinite lattice cases. However, the critical values of the coupling
of the continuum field theory, in the large $ N $ limit, is finite in the
infinite lattice case and zero in the case of finite lattice.
