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abstract: 'In these notes, the application of Feynman’s sum-over-paths approach to thermal phase transitions is discussed. The paradigm of such a spacetime approach to critical phenomena is provided by the high-temperature expansion of spin models. This expansion, known as the hopping expansion in the context of lattice field theory, yields a geometric description of the phase transition in these models, with the thermal critical exponents being determined by the fractal structure of the high-temperature graphs. The graphs percolate at the thermal critical point and can be studied using purely geometrical observables known from percolation theory. Besides the phase transition in spin models and in the closely related $\phi^4$ theory, other transitions discussed from this perspective include Bose-Einstein condensation, and the transitions in the Higgs model and the pure U(1) gauge theory.'
address:
- 'Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany'
- 'Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany'
author:
- Wolfhard Janke
- 'Adriaan M. J. Schakel'
date: 'July 11, 2006'
---

SPACETIME APPROACH TO PHASE TRANSITIONS
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Introduction
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Feynman’s spacetime approach to quantum mechanics provides a marvelously intuitive, yet computationally powerful entry to the quantum world.[@Feynman48] In this 