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- 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) = limn→∞ P (G, q), 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 qs, the following limits do not commute: limn→∞ limq→qs P (G, q) 1/n 6= limq→qs limn→∞ P (G, q).… (More)

We define an infinite set of families of graphs, which we call p-wheels and denote (Wh) n , that generalize the wheel (p = 1) and biwheel (p = 2) graphs. The chromatic polynomial for (Wh) 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, ...p+ 2 for… (More)

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy S0 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)

- A G Cunha-Netto, A A Caparica, Shan-Ho Tsai, Ronald Dickman, D P Landau
- Physical review. E, Statistical, nonlinear, and…
- 2008

Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) is shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using… (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. ∗email: shrock@insti.physics.sunysb.edu ∗∗email: tsai@insti.physics.sunysb.edu Nonzero ground state disorder and associated entropy, S0 6= 0, is an… (More)

- Shan-Ho Tsai
- 1998

Fourth-order cumulants of physical quantities have been used to characterize the nature of a phase transition. In this paper we report some Monte Carlo simulations to illustrate the behavior of fourth-order cumulants of magnetization and energy across second and rstorder transitions in the phase diagram of a well known spin-1 Ising model. Simple ideas from… (More)

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 S0/kB = 0.507(10) and discuss this result. ∗email: shrock@insti.physics.sunysb.edu ∗∗email:… (More)

- David P. Landau, Fugao Wang, Shan-Ho Tsai
- Computer Physics Communications
- 2008