Critical behavior of the two-state doubling algorithm
David M. Isaacson, Eli L. Isaacson, D. Marchesin, P. J. Paes-Leme · Journal of Mathematical Physics · 1983
We describe an algorithm which produces K2×K2 matrix approximations to the low energy part of the Schrödinger operator for N coupled oscillators. We carry out the algorithm analytically in the case K=2, for arbitrary N. In particular we show explicitly in this case how the N→∞ limit exhibits critical behavior.