We report on an experimental observation of self-organized criticality in ${}^4$He very close to its superfluid transition. A constant temperature gradient, independent of the heat flux $Q$ through the sample, is created along a vertical column of ${}^4$He by applying heat to the top of the column. This constant temperature gradient equals the gravity-induced gradient in the superfluid transition temperature, indicating that the thermal conductivity of the sample has self-organized. The closeness to criticality in this state is the same throughout most of the sample, and it depends only on $Q$.

• Received 9 January 1997

DOI:https://doi.org/10.1103/PhysRevLett.78.2421