HW2 - L appa (Max. Height) Max. Height 4 0.8 207 +/- 33...

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Sheet1 Page 1 HOMEWORK #2 Jorge Hernan Lopez Problem 1. Using the formula given I got the following autocorrelation times (τo) For the Energy κappa δplateau δzerobin τo 0.2 0.021 0.014 0.63 0.3 0.031 0.02 0.7 0.4 0.035 0.021 0.89 0.5 0.045 0.024 1.26 0.6 0.093 0.032 3.72 0.7 0.14 0.042 5.06 0.8 0.07 0.027 2.86 0.9 0.073 0.034 1.8 1 0.063 0.033 1.32 1.1 0.056 0.032 1.03 1.2 0.036 0.022 0.84 1.3 0.038 0.021 1.14 1.4 0.035 0.021 0.89 1.5 0.038 0.021 1.14 For the Magnetization κappa δplateau δzerobin τo 0.2 0.065 0.026 2.63 0.3 0.087 0.031 3.44 0.4 0.14 0.038 6.29 0.5 0.26 0.052 12 0.6 0.55 0.076 25.69 0.7 1.08 0.11 47.7 0.8 1.37 0.12 64.67 0.9 0.038 0.015 2.71 1 0.027 0.013 1.66 1.1 0.022 0.012 1.18 1.2 0.019 0.011 0.99 1.3 0.018 0.01 1.12 1.4 0.017 0.0094 1.14 1.5 0.016 0.0089 1.12 Problem 2. Below are showed the respective graphs. We clearly see that the autocorrelation time is very
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Sheet1 Page 2 high close to the phase transition. Problem 3. By using the procedure seen in lecture 8 I got the results shown below.
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Unformatted text preview: L appa (Max. Height) Max. Height 4 0.8 207 +/- 33 Sheet1 Page 3 6 0.7 787 +/- 109 8 0.7 1156 +/- 180 10 0.6 915 +/- 51 12 0.6 1296 +/- 75 We need to get a and b that best fits the relation e^bL^a=s, where s is the Susceptibility I use Curve-Fitting with Gnuplot for the relation ln(y) = a*lnx + b, where y=s and x+=L. I got the results Final set of parameters Asymptotic Standard Error a = 1.49685 +/- 0.4618 (30.85%) B = 3.59233 +/- 0.9441 (26.28%) Unfortunately we got a relatively high uncertainty. However it is in the appropriate range Finally we have for the ratio / the value 1.50 +/- 0.46 Sheet1 Page 4 http://www.phy.syr.edu/~abaskara/SPP_popular.html Sheet1 Page 5 Sheet1 Page 6...
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HW2 - L appa (Max. Height) Max. Height 4 0.8 207 +/- 33...

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