  We consider self-adjoint unbounded Jacobi matrices with diagonal q_n=n and
weights \lambda_n=c_n n, where c_n is a 2-periodical sequence of real numbers.
The parameter space is decomposed into several separate regions, where the
spectrum is either purely absolutely continuous or discrete. This constitutes
an example of the spectral phase transition of the first order. We study the
lines where the spectral phase transition occurs, obtaining the following main
result: either the interval (-\infty;1/2) or the interval (1/2;+\infty) is
covered by the absolutely continuous spectrum, the remainder of the spectrum
being pure point. The proof is based on finding asymptotics of generalized
eigenvectors via the Birkhoff-Adams Theorem. We also consider the degenerate
case, which constitutes yet another example of the spectral phase transition.
