Interface interactions in modulated phases, and upsilon points

Kevin E. Bassler, Kazuo Sasaki, Robert B. Griffiths

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy σ to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where σ=0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.

Original languageEnglish
Pages (from-to)45-88
Number of pages44
JournalJournal of Statistical Physics
Issue number1-2
Publication statusPublished - 1991 Jan 1
Externally publishedYes


  • Frenkel-Kontorova models
  • Modulated phases
  • commensurate-incommensurate transitions
  • interface interactions
  • interfaces

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Interface interactions in modulated phases, and upsilon points'. Together they form a unique fingerprint.

Cite this