Phase Transition in a Periodic Tubular Structure
Alexander V. Kiselev, Kirill Ryadovkin · SIAM Journal on Applied Mathematics · 2024
Abstract. We consider an [Formula: see text]-periodic ([Formula: see text]) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on [Formula: see text] which is fourth order at a discrete set of values of the magnetic potential ( critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases.