Short-distance behavior of the energy density near surfaces of critical systems

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Abstract
The critical behavior of the energy density near surfaces belonging to the surface universality classes called ordinary (O) and special (SB) transitions is investigated field theoretically. Both energy density profiles in a film and correlation functions in a half space of the energy density with other operators are considered right at O or SB criticality. We also discuss half-space profiles off criticality. Their properties are in accordance with the operator short-distance expansion of the energy density about the surface. Particular attention is paid to the occurrence of the component perpendicular to the surface of the stress tensor as a surface operator in these expansions.