Lambda point

The lambda point is the temperature at which normal fluid helium (helium I) makes the transition to superfluid state (helium II). At pressure of 1 atmosphere, the transition occurs at approximately 2.17 K. The lowest pressure at which He-I and He-II can coexist is the vapor−He-I−He-II triple point at 2.1768 K (−270.9732 °C) and 5.0418 kPa (0.049759 atm), which is the "saturated vapor pressure" at that temperature (pure helium gas in thermal equilibrium over the liquid surface, in a hermetic container).^[1] The highest pressure at which He-I and He-II can coexist is the bcc−He-I−He-II triple point with a helium solid at 1.762 K (−271.388 °C), 29.725 atm (3,011.9 kPa).^[2]

The point's name derives from the graph (pictured) that results from plotting the specific heat capacity as a function of temperature (for a given pressure in the above range, in the example shown, at 1 atmosphere), which resembles the Greek letter lambda ${\displaystyle \lambda }$. The specific heat capacity has a sharp peak as the temperature approaches the lambda point. The tip of the peak is so sharp that a critical exponent characterizing the divergence of the heat capacity can be measured precisely only in zero gravity, to provide a uniform density over a substantial volume of fluid. Hence, the heat capacity was measured within 2 nK below the transition in an experiment included in a Space Shuttle payload in 1992.^[3]

Although the heat capacity has a peak, it does not tend towards infinity (contrary to what the graph may suggest), but has finite limiting values when approaching the transition from above and below.^[3] The behavior of the heat capacity near the peak is described by the formula ${\displaystyle C\approx A_{\pm }t^{-\alpha }+B_{\pm }}$ where ${\displaystyle t=|1-T/T_{c}|}$ is the reduced temperature, ${\displaystyle T_{c}}$ is the Lambda point temperature, ${\displaystyle A_{\pm },B_{\pm }}$ are constants (different above and below the transition temperature), and α is the critical exponent: ${\displaystyle \alpha =-0.0127(3)}$.^[3][5] Since this exponent is negative for the superfluid transition, specific heat remains finite.^[6]

The quoted experimental value of α is in a significant disagreement^[7][4] with the most precise theoretical determinations^[8][9][10] coming from high temperature expansion techniques, Monte Carlo methods and the conformal bootstrap.