Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice

Details Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice

2000-04-11

arxiv.org/abs/cond-mat/0004161v2

Physica A290 (2001) 402-430

Physics

Condensed Matter

Statistical Mechanics

37 pages, latex, 4 encapsulated postscript figures

Scientific paper

10.1016/S0378-4371(00)00457-X

We present exact solutions for the zero-temperature partition function (chromatic polynomial $P$) and the ground state degeneracy per site $W$ (= exponent of the ground-state entropy) for the $q$-state Potts antiferromagnet on strips of the square lattice of width $L_y$ vertices and arbitrarily great length $L_x$ vertices. The specific solutions are for (a) $L_y=4$, $(FBC_y,PBC_x)$ (cyclic); (b) $L_y=4$, $(FBC_y,TPBC_x)$ (M\"obius); (c) $L_y=5,6$, $(PBC_y,FBC_x)$ (cylindrical); and (d) $L_y=5$, $(FBC_y,FBC_x)$ (open), where $FBC$, $PBC$, and $TPBC$ denote free, periodic, and twisted periodic boundary conditions, respectively. In the $L_x \to \infty$ limit of each strip we discuss the analytic structure of $W$ in the complex $q$ plane. The respective $W$ functions are evaluated numerically for various values of $q$. Several inferences are presented for the chromatic polynomials and analytic structure of $W$ for lattice strips with arbitrarily great $L_y$. The absence of a nonpathological $L_x \to \infty$ limit for real nonintegral $q$ in the interval $0 < q < 3$ ($0 < q < 4$) for strips of the square (triangular) lattice is discussed.

Affiliated with

Also associated with

No associations

Rating

Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-201706