Ising/Potts model applet: renormalization group algorithm
This applet implements a very simple version of the numeric renormalization group (RG) algorithm. The renormalization procedure is based on a majority rule and 2x2 plaquettes (check it by looking at the renormalized lattice in the right pane). In case of ambiguity, the renormalized spin value is drawn at random amongst the set of values in the original plaquette. The number of RG iterations can be changed from the "RG iterations" field. At each MC step, both the energy of the original lattice (the one being simulated) and of the renormalized lattice (displayed as E(RG)) are recorded. Both series are then averaged and displayed in the left-most chart in the south-panel. The point where the E and E(RG) curves cross represents an estimate of the RG fixed point. Applet help: The "temperature" button let you configure many things regarding the simulation, e.g. temperature sweep, number of thermalization steps, number of measurements, autocorrelation times, ... if the applet runs too slowly, reduce the "Latency". If still slow, deselect the "Animate" checkbox. The south-panel displays charts of thermodymical averages as a funtion of temperature. You can add a new point at any time during a simulation by clicking on the "Add point" button. If a temperature sweep is carried out, charts are filled automatically. Download source code : montecarlo.zip

S. Reynal (ENSEA/UCP)