CASIMIR TERMS AND SHAPE INSTABILITIES FOR 2-DIMENSIONAL CRITICAL SYSTEMS

We calculate the universal part of the free energy of certain finite t wo-dimensional regions at criticality by use of conformal field theory . Two geometries are considered: a section of a circle (''pie slice'') of angle phi and a helical staircase of finite angular (and radial) e xtent. We derive some consequences for certain matrix elements of the transfer matrix and corner transfer matrix. We examine the total free energy, including non-universal edge free energy terms, in both cases. A new, general, Casimir instability toward sharp corners on the bound ary is found; other new instability behavior is investigated. We show that at constant area and edge length, the rectangle is unstable again st small curvature.