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High Temperature Series Expansions for a Spin-One Model of Ferromagnetism
Get PDF[[abstract]]We have derived the first five terms of the high temperature series expansions of the dipole and quadrupole susceptibilities for an arbitrary lattice with pair interactions described by an isotropic spin one Hamiltonian H=-JΣijSi.Sj+αSi.Sj2. The dipole and quadrupole phase transition temperatures are determined from these series for a face centered cubic lattice for J>0 and for -0.51 the molecular field approximation predicts only quadrupole ordering. By using high temperature series we have not been able to ascertain whether there is any ordering of the dipoles at some temperature below the quadrupole ordering temperature TQ.[[fileno]]2010111010009[[department]]物理
High Temperature Susceptibility Series for the Spin-l/2 Anisotropic Heisenberg Model
Get PDF[[abstract]]The exact high temperature susceptibility series for the spin-1/2 uniaxially anisotropic Heisenberg model is derived through order T-7 for various lattices and anisotropies. The series is extrapolated by the Pade approximant method to give the critical parameters for a ferromagnet having spontaneous magnetization parallel to the symmetry axis of the system. When the anisotropy changes from the Ising limit to the isotropic Heisenberg limit the critical temperature of the system decreases, slowly in the Ising limit and rapidly in the isotropic limit. Our results are consistent with the hypothesis that the critical index remains constant as the anisotropy varies from the Ising limit toward the isotropic limit, and changes discontinuously when the system becomes isotropic.[[fileno]]2010111010012[[department]]物理
Numerical Representation and Identification of Graphs
Get PDF[[abstract]]A method to represent each linear graph by a single number, the determinant of its modified incidence matrix, is introduced. The isomorphism of graphs can be determined by comparing the determinants of their incidence matrices. Although it is not proved that different graphs can always be distinguished by the determinants of their modified incidence matrices, the proposed method provides a good practical algorithm for the identification of graphs. Applications of the single‐number representation of graphs are discussed.[[fileno]]2010111010025[[department]]物理
Low Temperature Behavior of a One-Dimensional Random Ising Model
No full text[[abstract]]The random Ising chain is a very simple model with a large number of metastable states. Simple analytical calculation of the relaxation of energy and magnetization is presented. The effect of a nonzero magnetic field is discussed qualitatively. The slow relaxation in this simple model resembles that observed in spin glasses. A weak magnetic field can produce rather strong effects. The magnetization is shown to be a nonanalytic function of the field. The field also greatly alters the metastability characteristics.[[fileno]]2010111010027[[department]]物理
Polarization of the Spin-S Exchange Interaction Model
Get PDF[[abstract]]The spin-S exchange interaction model of ferromagnetism is studied by the mean-field approximation. This model has 4S(S + 1) order parameters, and has infinitely many ground-state configurations. We define a single polarization parameter to describe the ordering of the system. Thermal variation of the polarization q(T) is determined for various spins. The phase transition is first order (except for S = 1/2) with phase transition temperature kT(c)/Jz = (2S - 1)/(4S ln2S), where z is the coordination number, and the discontinuity of q at T(c) is q(c) = (2S - 1)/2S.[[fileno]]2010111010044[[department]]物理
Cluster variation studies of the anisotropic exchange interaction model (vol 267, pg 153, 1999)
No full text[[fileno]]2010111010052[[department]]物理
Minimum Spanning Trees of Moving Points in the Plane
No full text[[abstract]]In this paper, we consider the following problem. Preprocess n moving points in the plane, such that the Euclidean minimum spanning tree of these points at a given time t can be reported efficiently. In our result, if the moving points are in k-motion, after an O(kn4 log n) time preprocessing step, and using O(m) space to store the preprocessing result, the Euclidean minimum spanning tree at a given time t can be reported in O(n) time, where m denotes the number of changes of the Euclidean minimum spanning tree of these points from time t = 0 to time t = infinity.[[fileno]]2030256010044[[department]]資訊工程學
On the Optimal Solution to AND/OR Series Parallel Graphs
No full text[[abstract]]This paper is concerned with efficient ways to find optimal solutions to AND/OR graphs. Although the general methods are still at large, we have found an efficient way to obtain optimal solutions to AND/OR series-parallel graphs. This is achieved by reducing an AND/OR series-parallel graph to an AND/OR tree. Once a graph is reduced to a tree, all the known exact and heuristic methods of tree searching can be applied.[[fileno]]2030256010059[[department]]資訊工程學
Parallel Algorithms for Computing the Closest Visible Vertex Pair Between Two Polygons
No full text[[abstract]]In this paper, we are concerned with the closest visible vertex pair problem, which is defined as follows: we are given two simple non-intersecting polygons P and Q with m and n vertices respectively, we are asked to find a closest visible pair of vertices between P and Q. We shall show that we can solve this problem in O(log(m+n)) time with O(m+n) processors in the CREW PRAM model.
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218195992000093[[fileno]]2030256010073[[department]]資訊工程學
Re-Os Systematics in Pallasites and and Mesosiderites
No full text[[abstract]]Re-Os on metal extracted from pallasites and mesosiderites and on the Bencubbin breccia is reported. The pallasites analyzed include Eagle Station and five members of the Main Group pallasites. Re-Os data on pallasites yield a slope and age which are identical to those for the IIAB isochron. The mesosiderites show a very limited range in Re-Os and do not permit an independent whole-rock isochron determination.[[fileno]]2010101030004[[department]]物理