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 Template:Convert and Template:Convert, which is the "saturated vapor pressure" at that temperature (pure helium gas in thermal equilibrium over the liquid surface, in a hermetic container).<ref name=Donnelly>Template:Cite journal</ref> 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 Template:Convert, Template:Convert.<ref name=Hoffer>Template:Cite journal</ref>
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 <math>\lambda</math>. 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.<ref name=JPL>Template:Cite journal</ref>Template:Unsolved
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.<ref name=JPL /> The behavior of the heat capacity near the peak is described by the formula <math>C\approx A_\pm t^{-\alpha}+B_\pm</math> where <math>t=|1-T/T_c|</math> is the reduced temperature, <math>T_c</math> is the Lambda point temperature, <math>A_\pm,B_\pm</math> are constants (different above and below the transition temperature), and Template:Math is the critical exponent: <math>\alpha=-0.0127(3)</math>.<ref name=JPL /><ref>Template:Cite journal</ref> Since this exponent is negative for the superfluid transition, specific heat remains finite.<ref>For other phase transitions <math>\alpha</math> may be positive (e.g. <math>\alpha\approx+0.1</math> for the liquid-vapor critical point which has Ising critical exponents). For those phase transitions specific heat does tend to infinity.</ref>
The quoted experimental value of Template:Math is in a significant disagreement<ref>Template:Cite book</ref><ref name="Rychkov">Template:Cite journal</ref> with the most precise theoretical determinations<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> coming from high temperature expansion techniques, Monte Carlo methods and the conformal bootstrap.