English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we compare the integrable hard hexagon model with thenon-integrable hard squares model by means of partition function roots andtransfer matrix eigenvalues. We consider partition functions for toroidal,cylindrical, and free-free boundary conditions up to sizes $40\times40$ andtransfer matrices up to 30 sites. For all boundary conditions the hard squaresroots are seen to lie in a bounded area of the complex fugacity plane alongwith the universal hard core line segment on the negative real fugacity axis.The density of roots on this line segment matches the derivative of the phasedifference between the eigenvalues of largest (and equal) moduli and exhibitsmuch greater structure than the corresponding density of hard hexagons. We alsostudy the special point $z=-1$ of hard squares where all eigenvalues have unitmodulus, and we give several conjectures for the value at $z=-1$ of thepartition functions.

Integrability vs non-integrability: Hard hexagons and hard squares compared