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Statistical physics models on multi-page books exhibit discontinuous phase transitions, even for models with continuous transitions. This occurs when the number of pages is large, as demonstrated with the Ising model on a three-page book.

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Area of Science:

  • Statistical physics
  • Mathematical physics
  • Condensed matter theory

Background:

  • Statistical physics models often exhibit continuous phase transitions on simple geometries.
  • The behavior of these models on complex or non-Euclidean spaces is less understood.
  • Previous theoretical work suggested altered phase transition properties in such systems.

Purpose of the Study:

  • To investigate the phase transition behavior of statistical physics models on a 'book' geometry (pages as half-planes).
  • To determine if continuous phase transitions can become discontinuous on this book manifold.
  • To analyze the Ising model specifically on a three-page book.

Main Methods:

  • Mathematical analysis of statistical physics models.
  • Investigation of models on a manifold composed of half-planes (book geometry).
  • Focus on the Ising model with specific coupling constants.

Main Results:

  • Models undergoing continuous phase transitions on a plane exhibit discontinuous transitions on a book with sufficient pages.
  • The Ising model on a three-page book demonstrates a discontinuous phase transition.
  • This finding is contingent on considering large coupling constants at page interfaces.

Conclusions:

  • The geometry of the space significantly impacts phase transition properties in statistical physics.
  • A 'book' manifold can induce discontinuities in phase transitions that are continuous in simpler spaces.
  • Results align with and confirm prior theoretical predictions from renormalization group and conformal field theory.