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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)
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 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)
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)
We present extensive Monte Carlo spin-dynamics simulations of the vector Blume-Emery-Griffiths model with three-dimensional spins on a simple cubic lattice and periodic boundary conditions. For a range of Hamiltonian parameters, this model reproduces the phase diagram topology of the one experimentally observed for bulk mixtures of 3He-4He . Highly(More)