有限尺寸标度与相变 - 上海交通大学物理系.ppt

* We used a cluster algorithm for the calculation. * * * * * * * * * * * * T is not fixed and is usually zero unless X’ is in a “neighborhood” of X. Show that detailed balance equation is satisfied. Peskun has a theorem which says, in some sense, Metropolis rate min(1, …) is most efficient. P Peskun, Biometrika, 60 (1973) 607. * Typical modern calculation takes 106 of sweeps and still hours to days to complete. Number of particles can be 1000 to a million. * Mathematical Analyzer Numerator Integrator and Computer--a low-tech name for what was in its time a very high-tech piece of equipment. MANIAC was a computer built at the Los Alamos Scientific Laboratory in the late 1940s and early 1950s. Its mostly remembered today for its use in the development of the hydrogen bomb. Picture from /maniac.html * In 1925, physicist W. Lenz asked his student E. Ising to solve a statistical mechanics problem relevant to the magnetic properties of matter. Ising was able to solve it on a one-dimensional lattice. Almost twenty years were passed before L. Onsager found analytic solution to the two-dimensional version of the problem. The three-dimensional Ising model which is most relevant in the physical world has denied any serious attempt. Thus, any information we have is from approximations and numerical simulations. Ising model and its generalizations are extremely important in our understanding of the properties of matter, especially the phenomena of phase transitions. Ising model is still actively used in various ways to model systems in condensed matter physics. * For finite system it does make a difference between M with absolute value and without. * Susceptibility above is for zero field, B=0. 4th order cumulant can be used to determine Tc, by the crossing of curves from different systems. * * * * * * * * * * * * * * * * * * * * * * * * * α, β, γ, and ν are known as critical exponents. To derive the results, we need to use the thermodynamic relation between free ene