Phase Transition in a Periodic Tubular Structure

Alexander V. Kiselev, Kirill Ryadovkin

Research output: Contribution to journalArticlepeer-review


We consider an ε-periodic (ε→0) tubular structure, modelled 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 R which is fourth order at a discrete set of values of the magnetic potential (\emph{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.
Original languageEnglish
Pages (from-to)890-914
Number of pages25
JournalSIAM Journal on Applied Mathematics
Issue number3
Early online date6 May 2024
Publication statusPublished - 30 Jun 2024

Data Availability Statement

No new data were generated or analyzed during this study.


  • asymptotic analysis
  • homogenization
  • periodic graphs
  • phase transitions

ASJC Scopus subject areas

  • Applied Mathematics

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