Long-Range Order for Critical Book-Ising and Book-Percolation

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.