
GEOMETRICAL APPROACH TO PHASE TRANSITIONSAdriaan SchakelInstitut für Theoretische Physik, Universität LeipzigUsing percolation theory as a paradigm, a geometrical approach to phase transitions is developed. The theory is worked out explicitly for the twodimensional Ising modelone of the simplest statistical models exhibiting nontrivial critical behavior. Other systems considered include BoseEinstein condensates (BEC) and superfluid He4. It is shown that the fractal dimensions of the relevant geometrical objects (Peierls domain walls in the Ising model, worldlines in BEC, vortex loops in superfluid He) encode the critical exponents. The lectures are physically intuitive and nontechnical in nature.See also: [1] A. Schakel. Entangled Vortices: Onsager's geometrical picture of superfluid phase transitions. J. Low Temp. Phys. 129 (2002) 323. [2] W. Janke, A.M.J. Schakel. Geometrical vs. FortuinKasteleyn clusters in the twodimensional qstate Potts model. Nucl. Phys. B, 700 (2004) 385. Personal webpage 