Ground state entropy in Potts antiferromagnets

Robert Shrock

Physica A: Statistical Mechanics and its Applications, 2000, vol. 281, issue 1, 221-232

Abstract: The q-state Potts antiferromagnet exhibits nonzero ground state entropy S0({G},q)≠0 for sufficiently large q on a given n-vertex lattice Λ or graph G and its n→∞ limit {G}. We present exact calculations of the zero-temperature partition function Z(G,q,T=0) and W({G},q), where S0=kBlnW, for this model on a number of families G. These calculations have interesting connections with graph theory, since Z(G,q,T=0)=P(G,q), where the chromatic polynomial P(G,q) gives the number of ways of coloring the vertices of the graph G such that no adjacent vertices have the same color. Generalizing q from Z to C, we determine the accumulation set B of the zeros of P(G,q), which constitute the continuous loci of points on which W is nonanalytic. The Potts antiferromagnet has a zero-temperature critical point at the maximal value qc where B crosses the real q-axis. In particular, exact solutions for W and B are given for infinitely long, finite-width strips of various lattices; in addition to their intrinsic interest, these yield insight into the approach to the 2D thermodynamic limit. Some corresponding results are presented for the exact finite-temperature Potts free energy on families of graphs. Finally, we present rigorous upper and lower bounds on W for 2D lattices.

Keywords: Potts model; Spin models; Chromatic polynomials (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437100000236
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:281:y:2000:i:1:p:221-232

DOI: 10.1016/S0378-4371(00)00023-6

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().