NDLI: Hard Squares for z =

Content Provider	Springer Nature Link
Author	Baxter, R. J.
Copyright Year	2011
Abstract	The hard square model in statistical mechanics has been investigated for the case when the activity z is −1. For cyclic boundary conditions, the characteristic polynomial of the transfer matrix has an intriguingly simple structure, all the eigenvalues x being zero, roots of unity, or solutions of x 3 = 4cos2(πm/N). Here we tabulate the results for lattices of up to 12 columns with cyclic or free boundary conditions and the two obvious orientations. We remark that they are all unexpectedly simple and that for the rotated lattice with free or fixed boundary conditions there are obvious likely generalizations to any lattice size.
Ending Page	195
Page Count	11
Starting Page	185
File Format	PDF
ISSN	02180006
e-ISSN	02193094
Journal	Annals of Combinatorics
Issue Number	2
Volume Number	15
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-06-05
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	lattice models Exact enumeration problems, generating functions Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs transfer matrices Combinatorics statistical mechanics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics

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Hard Squares for z = –1