P. Kleban et I. Peschel, CASIMIR TERMS AND SHAPE INSTABILITIES FOR 2-DIMENSIONAL CRITICAL SYSTEMS, Zeitschrift fur Physik. B, Condensed matter, 101(3), 1996, pp. 447-453
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.