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Getting Started

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 * Compressed lecture notes (No virus!)
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Numerical Recipes:

 * 7.7 Simple monte carlo integration

Concepts:

 * Damage spreading
 * set spins at T_min to 1 and 2 respectively for two separate runs
 * after reaching equilibrium see how the two systems differ, record in a table //d(i,j)//
 * use this to identify the ordered state ie its interface
 * search along each row from //high// temperature for first spin that differ ( //d(i,j) == 1 )//
 * record the column in the interface profile I(j)
 * Statistics, mean and variance can be obtained from I(j) at different instants

__**Pseudo code / procedure**__ > Initialize two identical spin glass copies > Lock spins to 1 and 2 along the column with T = T(min) > Evolve according to HB using the same random numbers until having reached steady state (do not update spins at the columns with Tmax, Tmin) > Start recording differences between the two systems > Assign d(i,j) a value of 1 if the spins are different at (i,j) and zero if they are equal > At regular intervals do: > > for i = 1 to L > for j = L to 0 > if (d(i,j) == 1) I(i) = j; > end > end > > Calculate W (the standard deviation of I(j)) > Plot W as a function og g, the temperature gradient in log-log. > The slope is exponent - v/(1 + v), from which v (the critical exponent) is derived. > Calculate Teff as a function og g^(1/v), Teff = Tc at the y intercept (where g^(1/v) = 0) > Heat Bath (HB): > Choose a node (i,j) at random > Assign s(i,j) a value q in the range [1,Q] with probability p(q) given by (13)