| Feynman's sum-over-paths approach to quantum mechanics is applied to thermal phase transitions. Examples of such a spacetime description are provided by the high-temperature expansion of spin models, and by Feynman's explanation of Bose-Einstein condensation in terms of particle exchange rings. A purely geometric approach emerges, in which phase transitions are signaled by a proliferation of paths. Being geometrical objects, their analysis is amenable to the methods developed in percolation theory. The critical exponents are determined by the fractal structure of the paths, which can be studied by simulating the trajectories directly. Applications of such geometric Monte Carlo simulations in the context of spin models are presented. Other transitions discussed from the spacetime perspective include the deconfinement transition in the compact Abelian Higgs model. |
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