Journal article
Integrability versus non-integrability: hard hexagons and hard squares compared
M Assis, JL Jacobsen, I Jensen, JM Maillard, BM McCoy
Journal of Physics A Mathematical and Theoretical | Published : 2014
Abstract
In this paper we compare the integrable hard hexagon model with the non-integrable hard squares model by means of partition function roots and transfer matrix eigenvalues. We consider partition functions for toroidal, cylindrical, and free-free boundary conditions up to sizes 40 x 40 and transfer matrices up to 30 sites. For all boundary conditions the hard squares roots are seen to lie in a bounded area of the complex fugacity plane along with 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 phase difference between the eigenvalues of largest (and equal) moduli and exhibits much greater structure..
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Awarded by Australian Research Council
Funding Acknowledgements
We are pleased to acknowledge fruitful discussions with C Ahn, AJ Guttmann, and PA Pearce. One of us (JJ) is pleased to thank the Institut Universitaire de France and Agence Nationale de la Recherche under grant ANR-10-BLAN-0401 and the Simons Center for Geometry and Physics for their hospitality. One of us (IJ) was supported by an award under the Merit Allocation Scheme of the NCI National facility at the ANU and by funding under the Australian Research Council's Discovery Projects scheme by the grant DP140101110. We also made extensive use of the High Performance Computing services offered by ITS Research Services at the University of Melbourne.