The Casimir interaction between two thin material films, between a film and athick plate and between two films deposited on substrates is considered atlarge separations (high temperatures) which correspond to the classical limit.It is shown that the free energy of the classical Casimir interaction betweentwo insulating films with no free charge carriers and between an insulatingfilm and a material plate depends on film thicknesses and decreases withseparation more rapidly than the classical limit for two thick plates. The freeenergy of thin films characterized by the metallic-type dielectric permittivitydecreases as the second power of separation, i.e., demonstrates the standardclassical limit. The obtained results shed light on the possibility to describedispersion interaction between two graphene sheets and between a graphene sheetand a material plate by modeling graphene as a thin film possessing somedielectric permittivity. It is argued that the most reliable results areobtained by describing the reflection properties on graphene by means of thepolarization tensor in (2+1)-dimensional space-time.
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