Quantum phase transitions in alternating transverse Ising chains:   Rigorous analytical and exact numerical results
  We examine the ground state properties of the s=1/2 transverse Ising chain with regularly alternating bonds and fields using exact analytical results and exact numerical data for long (up to N=900) and short (N=20) chains. For a given period of alternation the system may exhibit a series of quantum phase transitions, where the number of transitions depends on the concrete set of the parameters of the Hamiltonian. The critical behaviour for the nonuniform and the uniform chain is the same. 
Oleg Derzhko, Johannes Richter, Taras Krokhmalskii and Oles'   Zaburannyi