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We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy S 0 for the q-state Potts antiferromagnet on families of cyclic and twisted cyclic (Möbius) strip graphs composed of p-sided polygons. Our results suggest a general rule concerning the maximal region in the complex q… (More)

- Shan-Ho Tsai, M. Krech, D. P. Landau
- 2003

We review recently developed decomposition algorithms for molecular dynamics and spin dynamics simulations of many-body systems. These methods are time reversible, symplectic, and the error in the total energy thus generated is bounded. In general, these techniques are accurate for much larger time steps than more standard integration methods. Illustrations… (More)

We study the asymptotic limiting function W ({G}, q) = lim n→∞ P (G, q) 1/n , where P (G, q) is the chromatic polynomial for a graph G with n vertices. We first discuss a subtlety in the definition of W ({G}, q) resulting from the fact that at certain special points q s , the following limits do not commute: lim n→∞ lim q→qs P (G, q) 1/n = lim q→qs lim n→∞… (More)

We define an infinite set of families of graphs, which we call p-wheels and denote (W h) (p) n , that generalize the wheel (p = 1) and biwheel (p = 2) graphs. The chromatic polynomial for (W h) (p) n is calculated, and remarkably simple properties of the chromatic zeros are found: (i) the real zeros occur at q = 0, 1, ...p + 1 for n − p even and q = 0, 1,… (More)

- Shan-Ho Tsai
- 1997

We derive rigorous upper and lower bounds for the ground state entropy of the q-state Potts antiferromagnet on the honeycomb and triangular lattices. These bounds are quite restrictive, especially for large q.

We show an exact equivalence of the free energy of the q-state Potts antiferromagnet on a lattice Λ for the full temperature interval 0 ≤ T ≤ ∞ and the free energy of the q-state Potts model on the dual lattice for a semi-infinite interval of complex temperatures (CT). This implies the existence of two quite different types of CT singularities: the generic… (More)

We study the q-state Potts antiferromagnet with q = 3 on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all T ≥ 0. We also calculate the ground state entropy to be S 0 /k B = 0.507(10) and discuss this result.