03-24E

We discuss the effects of the regularly alternating Hamiltonian parameters on the quantum (zero-temperature) phase transition inherent in the spin-$\frac {1}{2}$ transverse Ising chain. We demonstrate that for a given period of alternation the number of quantum phase transition points is strongly parameter dependent. The critical behavior remains as that of the uniform chain. However, weak singularities may occur as well. We also provide a pedagogical introduction to the quantum phase transition theory as well as present some details of the calculations performed. This is the lecture given at the 5th Small Triangle Meeting on Theoretical Physics (Medzev, Slovakia, September 2-4, 2003).