Long-range order for critical Book-Ising and Book-percolation

TL;DR

This paper demonstrates that statistical physics models like the Ising and percolation models exhibit a transition from continuous to discontinuous phase transitions when placed on a multi-page book structure, confirming theoretical physics predictions.

Contribution

It proves that the phase transition nature changes to discontinuous for models on a multi-page book, extending understanding of phase transitions in complex geometries.

Findings

Discontinuous phase transition for Ising model on three-page book.

Phase transition behavior depends on the number of pages.

Supports predictions from renormalization group and conformal field theory.

Abstract

In this paper, we investigate the behaviour of statistical physics models on a book with pages that are isomorphic to half-planes. We show that even for models undergoing a continuous phase transition on $\mathbb Z^2$, the phase transition becomes discontinuous as soon as the number of pages is sufficiently large. In particular, we prove that the Ising model on a three pages book has a discontinuous phase transition (if one allows oneself to consider large coupling constants along the line on which pages are glued). Our work confirms predictions in theoretical physics which relied on renormalization group, conformal field theory and numerics ([Car91,ITB91,SMP10]) some of which were motivated by the analysis of the Renyi entropy of certain quantum spin systems.