Boutroux curves

Here below you see the surface of the real part of the g-function for the potential and some choice of contours of integration.

Nice movies of Boutroux curves undergoing phase transistions

The animations are made frame-by-frame with some Octave code of my production. They are then converted to jpg and into a compressed mpeg4 (or some similar format) using mencoder. All software used is open source.

Mac Users: you may need the QuickTime plugin Flip4Mac that is available for free (install it and quit Safari, then reopen).
Windows users: you are on your own, sorry!

The ``blurred'' lines in the inmost parts of the tree are just numerical artifacts; ideally the arcs should cleanly connect the vertices (marked with little crosses).

In the two animations that are (should be) running on the left you see a typical transition. When the saddle point (the node with four legs) intersects the cut the first solution glues to the second solution.

The potential is fixed to

and the total charge (mass of the measure) is T ranging from 3 down to 1 in both animations.

Another example for a degree 4 potential is found here