Abstract
We have measured the specific heat of helium near the superfluid transition for films up to 56 A thick and for sample confined to a cylindrical geometry of up to 2000 A in diameter. The dependence of the shift in the transition temperature on size and the growth of the specific-heat maximum do not yield exponents as expected from simple scaling arguments. The data up to t equivalent abs. value(1 - T/T/sub lambda/) = 10/sup -2/ scale according to a form suggested by Fisher, but with an exponent 1/theta = 0.54 +- 0.02.
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