Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spacetime Approach to Phase Transitions   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.

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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc