An exactly solvable model of randomly pinned charge density waves in two dimensions

Matthew C. O’Brien, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-N technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii-Kosterlitz-Thouless phase transition in the clean limit at large N. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.

Original languageEnglish (US)
Article number013104
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number1
StatePublished - Jan 1 2024


  • cavity and replica method
  • exact results
  • random field Ising models
  • randomly pinned density waves

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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