1 h) Mean cluster size - Githubissues

You are now ready to do your first large scale Monte Carlo simulation. The phys- ical property of interest is the mean cluster size, ⟨d⟩, where the size of a cluster is defined as the total number of monomers belonging to the cluster. In the next sim- ulation, use N = 15, M = 25. Consider 10 evenly spaced temperatures between Tl = 100 K and Th = 1000 K. As discussed in subsection 3.3, it is necessary to let the system reach its equilibrium before you start making measurements. Choose t_equil(T) = t_max exp(−s(T − Tl)) + C with t_max = 100000, s = 1/200, C = 10 000, as this will result in reasonable run times. Note that this is a slightly optimistic estimate for how many MC steps that are required to reach equilibrium for low temperatures, so if the run time is manageable, you might consider to increase t_max. However, if the run time of your code with t_max is too long, you may use a lower value. Use t_r = 1000, and choose a suitable n. Use different initial grids at different temperatures.

Plot ⟨d⟩ as a function of T. Why is ⟨d⟩ larger at small T ? Discuss if your choice of n will yield reliable results. Are any of your results surprising? In order to observe how the initial conditions of the grid affects the clustering size, redo the simulation, and compare the results of the two simulations. Why is the discrepancy between the simulations larger at lower temperatures?

martinsw01 / vitber-bio

1 h) Mean cluster size #9