  We consider the spin-1/2 Ising chain in a regularly alternating transverse
field to examine the effects of regular alternation on the quantum phase
transition inherent in the quantum Ising chain. The number of quantum phase
transition points strongly depends on the specific set of the Hamiltonian
parameters but never exceeds 2p where p is the period of alternation.
Calculating the spin correlation functions numerically (for long chains of up
to 5400 sites) and determining the critical exponents we have demonstrated that
two types of critical behavior are possible. In most cases the square-lattice
Ising model universality class occurs, however, a weaker singularity may also
take place.
