Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Spontaneous Symmetry Breaking for Film System Within Scalar
  $\phi^4$ Model for Phase Transition   The difficulty is analysed in evaluating fluctuations in phase transition of
finite-size system at temperature far below the critical point. Film system is
discussed with one-component order parameter $\phi^4$ model for phase
transition. Non-trivial vacuum state corresponding to minimum Hamiltonian is
given approximately for various boundary conditions. It is shown that the
spontaneous symmetry breaking plays an important role for such systems, and
that perturbative calculations can be done safely when the effect of the vacuum
state or the local spontaneous symmetry breaking is taken into consideration.

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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: econ