This repo is for the code written for the Computational Lab at University of Pisa. This is a work in progress, the main topic will be the implementation of the Propp-Wilson algorithm for the study of the Ising model.

Keywords: Propp-Wilson, Markov chain, MCMC, Coupling from the past, Ising model, Random Cluster, Fortune, Edwards, Phase Transition

HERE you can find the report I wrote (in Italian).

A short description of the scripts:

• configuration_cluster.py: Uses Propp-Wilson with clusters to plot a configuration of the Ising model at given N and beta
• cluster_times.py: plot on a log scale the number of step needed for coalescence using cluster.
• cluster.py: Uses clusters for the Ising model on a torus grid.
• graph_cluster.py: Failed attempt to use the hdtgraph package to speedup the computation with the connected components of the graph.
• ising_mag.py: uses propp-wilson without clusters, plots the magnetization as a function of beta.
• grid_clustered.py: same as ising_mag, but uses clusters.
• pw_times.py: as as cluster_times, but without clusters.
• ssh_download.sh: small utily script for downloading results from a server.
• plotter.py: plots data from csv file
• multi_ising_mag.py: same as ising_mag, but can run on multiple processors at the same time.

Warning: I haven't reverified the next ones! They may not work.

• vanilla_mcmc.py: here I use a simple Monte Carlo method with Markov Chains for generating a target distribution over a finite set of states.
• simple_pw.py: as the name says, it is a Propp Wilson that runs all the N chains, with the same distributions of vanilla_mcmc.
• false_pw.py: same as simple_pw, but this one regenerates all the random values. It shouldn't work.
• monotone_pw.py: implements the sandwiching method with a linear chain.
• monotone_legth_pw.py: same as above, but plots the numbers of steps needed for convergence.
• simple_ising.py: it is a simple ising model, with the pw algorithm. Prints the log of the number of steps needed for coalescence and the ratio between the number of +1 and the total number of nodes.
• ising_depth.py: this one runs multiple ising simulations and plot the log of the steps needed for coalescence as a function of beta. It works more or less for N<40 and beta<0.3.
• ising_frac.py: same as above, but plots the fraction of +1 as a function of beta.