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.