First Order Phase Transition in the 3-dimensional Blume-Capel Model on a Cellular Automaton

The first order phase transition of the three-dimensional Blume Capel are investigated using cooling algorithm which improved from Creutz Cellular Automaton for the $D/J=2.9$ parameter value in the first order phase transition region. The analysis of the data using the finite-size effect and the histogram technique indicate that the magnetic susceptibility maxima and the specific heat maxima increase with the system volume ($L^{d}$) at $$.Comment: 13 pages, 4 figure

The Critical Behaviour of the Spin-3/2 Blume-Capel Model in Two Dimensions

The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance and Monte Carlo simulations. The model in its $\tau$-continuum Hamiltonian version is also considered and compared with others spin-3/2 quantum chains. Our results indicate that differently from the standard spin-1 Blume-Capel model there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean field prediction but in disagreement with previous approximate renormalization group calculations. We also presented new results for the spin-1 Blume-Capel model.Comment: latex 18 pages, 4 figure

Learning, Experimentation, and Long-Run Behavior in Games

This paper investigates a class of population-learning dynamics. In every period agents either adopt a best reply to the current distribution of actual play, or a best reply to a sample, taken with replacement, from the distribution of intended play (the strategies adopted at the end of last period), or they are inactive. If sampling with replacement and being inactive have strictly positive probability, these dynamics converge globally to minimal curb sets in the absence of mistakes. For two-player i x j-games, i; j .le. 3; the same result holds even if only best responding to actual play and being inactive have positive probability. If players make mistakes in the implementation of their strategies, these dynamics select among minimal curb sets .

Surface reentrance in the semi-infinite spin-1 Ising models

The critical behavior of the semi-infinite Blume-Capel and Blume-Emery-Griffiths models is investigated in the pair approximation of the Cluster Variation Method. Equations for bulk and surface order parameters and n.n. correlation functions are given, from which analytical expressions for the second order bulk and surface critical temperatures are derived. The phase diagrams of the Blume-Capel model are classified, and the existence of a surface first order transition is discussed. This transition is shown to be, under certain conditions, slightly reentrant, and the behavior of the surface order parameters and correlation functions is given for such a case. The extension of our results to the Blume-Emery-Griffiths model is briefly discussed.Comment: 17 pages, 14 figures (PostScript, appended), POLFIS-TH.19/9

Reentrant Phase Transitions of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

The spin-1 Ising (BEG) model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton(CCA) for a simple cubic lattice. The simulations have been made for several sets of parameters $K/J$ and $D/J$ in the $-3<D/J\leq 0$ and $-1\leq K/J\leq 0$ parameter regions. The re-entrant and double re-entrant phase transitions of the BEG model are determined from the temperature variations of the thermodynamic quantities ($M$, $Q$ and $\chi$). The phase diagrams characterizing phase transitions are compared with those obtained from other methods.Comment: 12 pages 7 figure

Civil Procedure And Evidence—Res Judicata

Maflo Holding Corp. v. S. J. Blume Inc., 308 N. Y. 570, 127 N. E. 2d 558 (1955)