The Case of Critical Coupling in a Class of Unbounded Jacobi Matrices Exhibiting a First-Order Phase Transition

Details The Case of Critical Coupling in a Class of Unbounded Jacobi Matrices Exhibiting a First-Order Phase Transition The Case of Critical Coupling in a Class of Unbounded Jacobi Matrices Exhibiting a First-Order Phase Transition

2006-05-22

arxiv.org/abs/math/0605593v1

Mathematics

Spectral Theory

14 pages

Scientific paper

We consider a class of Jacobi matrices with unbounded coefficients. This
class is known to exhibit a first-order phase transition in the sense that, as
a parameter is varied, one has purely discrete spectrum below the transition
point and purely absolutely continuous spectrum above the transition point. We
determine the spectral type and solution asymptotics at the transition point.

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