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Course: CHE 524, Fall 2009School: Princeton
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524 Introduction CHE to Statistical Mechanics PROBLEM SET 5 Due: Tuesday, Nov. 25, 2008 Fall 2008 1. Write code to perform a Monte Carlo simulation of the 3-dimensional Ising model at zero field (H=0), in a cubic box of size L under periodic boundary conditions. Using any programming environment (e.g. C, Visual Basic, MATLAB, Fortran, Java ) available on a machine to which you have access (e.g. OIT clusters,...
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524
Introduction CHE to Statistical Mechanics PROBLEM SET 5 Due: Tuesday, Nov. 25, 2008
Fall 2008
1.
Write code to perform a Monte Carlo simulation of the 3-dimensional Ising model at zero field (H=0), in a cubic box of size L under periodic boundary conditions. Using any programming environment (e.g. C, Visual Basic, MATLAB, Fortran, Java ) available on a machine to which you have access (e.g. OIT clusters, your laptop etc). The code should produce a histogram f(M) for the magnetization. (a) For L=5, obtain and plot the magnetization normalized probability distribution f(M) for T/Tc=0.9, 1 and 1.1 [you may use Tc/kB= 4.4, in units of the energy]. nearestneighbor (b) Also for L=5, obtain and plot the energy normalized probability distribution g(U) for T/Tc=1 and 1.1 (c) Reweight the g(U) data of part (b) from T/Tc =1 to T/Tc = 1.1 and compare the reweighted and actual simulation data.
2.
(a) Obtain an expression and plot the radial distribution function for gaseous argon at T = 300 K, P = 1 bar. (b) Calculate (analytica...
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