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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 $\lambda$ . 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]

Unsolved problem in physics:

Explain the discrepancy between the experimental and theoretical determinations of the heat capacity critical exponent

α

for the superfluid transition in helium-4.^[4]

(more unsolved problems in physics)

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 $C\approx A_{\pm }t^{-\alpha }+B_{\pm }$ where $t=|1-T/T_{c}|$ is the reduced temperature, $T_{c}$ is the Lambda point temperature, $A_{\pm },B_{\pm }$ are constants (different above and below the transition temperature), and $α$ is the critical exponent: $\alpha =-0.0127(3)$ .^[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.

References

^ Donnelly, Russell J.; Barenghi, Carlo F. (1998). "The Observed Properties of Liquid Helium at the Saturated Vapor Pressure". Journal of Physical and Chemical Reference Data. 27 (6): 1217–1274. Bibcode:1998JPCRD..27.1217D. doi:10.1063/1.556028.
^ Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. (April 1976). "Thermodynamic properties of ⁴He. II. The bcc phase and the P-T and VT phase diagrams below 2 K". Journal of Low Temperature Physics. 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245. S2CID 120473493.
^ ^a ^b ^c Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. (1996). "Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point". Physical Review Letters. 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944. hdl:2060/19950007794. PMID 10061591. S2CID 29876364.
^ ^a ^b Rychkov, Slava (2020-01-31). "Conformal bootstrap and the λ-point specific heat experimental anomaly". Journal Club for Condensed Matter Physics. doi:10.36471/JCCM_January_2020_02.
^ Lipa, J. A.; Nissen, J. A.; Stricker, D. A.; Swanson, D. R.; Chui, T. C. P. (2003-11-14). "Specific heat of liquid helium in zero gravity very near the lambda point". Physical Review B. 68 (17): 174518. arXiv:cond-mat/0310163. Bibcode:2003PhRvB..68q4518L. doi:10.1103/PhysRevB.68.174518. S2CID 55646571.
^ For other phase transitions $\alpha$ may be negative (e.g. $\alpha \approx +0.1$ for the liquid-vapor critical point which has Ising critical exponents). For those phase transitions specific heat does tend to infinity.
^ Vicari, Ettore (2008-03-21). "Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories". Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007). Vol. 42. Regensburg, Germany: Sissa Medialab. p. 023. doi:10.22323/1.042.0023.
^ Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore (2006-10-06). "Theoretical estimates of the critical exponents of the superfluid transition in $^{4}\mathrm{He}$ by lattice methods". Physical Review B. 74 (14): 144506. arXiv:cond-mat/0605083. doi:10.1103/PhysRevB.74.144506. S2CID 118924734.
^ Hasenbusch, Martin (2019-12-26). "Monte Carlo study of an improved clock model in three dimensions". Physical Review B. 100 (22): 224517. arXiv:1910.05916. Bibcode:2019PhRvB.100v4517H. doi:10.1103/PhysRevB.100.224517. ISSN 2469-9950. S2CID 204509042.
^ Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro (2020). "Carving out OPE space and precise O(2) model critical exponents". Journal of High Energy Physics. 2020 (6): 142. arXiv:1912.03324. Bibcode:2020JHEP...06..142C. doi:10.1007/JHEP06(2020)142. S2CID 208910721.

External links

What is superfluidity?

[Donnelly-1] Donnelly, Russell J.; Barenghi, Carlo F. (1998). "The Observed Properties of Liquid Helium at the Saturated Vapor Pressure". Journal of Physical and Chemical Reference Data. 27 (6): 1217–1274. Bibcode:1998JPCRD..27.1217D. doi:10.1063/1.556028.

[Hoffer-2] Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. (April 1976). "Thermodynamic properties of ⁴He. II. The bcc phase and the P-T and VT phase diagrams below 2 K". Journal of Low Temperature Physics. 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245. S2CID 120473493.

[JPL-3] Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. (1996). "Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point". Physical Review Letters. 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944. hdl:2060/19950007794. PMID 10061591. S2CID 29876364.

[Rychkov-4] Rychkov, Slava (2020-01-31). "Conformal bootstrap and the λ-point specific heat experimental anomaly". Journal Club for Condensed Matter Physics. doi:10.36471/JCCM_January_2020_02.

[5] Lipa, J. A.; Nissen, J. A.; Stricker, D. A.; Swanson, D. R.; Chui, T. C. P. (2003-11-14). "Specific heat of liquid helium in zero gravity very near the lambda point". Physical Review B. 68 (17): 174518. arXiv:cond-mat/0310163. Bibcode:2003PhRvB..68q4518L. doi:10.1103/PhysRevB.68.174518. S2CID 55646571.

[6] For other phase transitions $\alpha$ may be negative (e.g. $\alpha \approx +0.1$ for the liquid-vapor critical point which has Ising critical exponents). For those phase transitions specific heat does tend to infinity.

[7] Vicari, Ettore (2008-03-21). "Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories". Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007). Vol. 42. Regensburg, Germany: Sissa Medialab. p. 023. doi:10.22323/1.042.0023.

[8] Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore (2006-10-06). "Theoretical estimates of the critical exponents of the superfluid transition in $^{4}\mathrm{He}$ by lattice methods". Physical Review B. 74 (14): 144506. arXiv:cond-mat/0605083. doi:10.1103/PhysRevB.74.144506. S2CID 118924734.

[9] Hasenbusch, Martin (2019-12-26). "Monte Carlo study of an improved clock model in three dimensions". Physical Review B. 100 (22): 224517. arXiv:1910.05916. Bibcode:2019PhRvB.100v4517H. doi:10.1103/PhysRevB.100.224517. ISSN 2469-9950. S2CID 204509042.

[10] Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro (2020). "Carving out OPE space and precise O(2) model critical exponents". Journal of High Energy Physics. 2020 (6): 142. arXiv:1912.03324. Bibcode:2020JHEP...06..142C. doi:10.1007/JHEP06(2020)142. S2CID 208910721.

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@@ Line 1: / Line 1: @@
+{{Short description|Superfluid transition temperature of helium-4}}
-[[File:Lambda transition.svg|thumb|250px|The plot of the specific heat capacity versus temperature]]
+[[File:Lambda transition.svg|thumb|250px|The plot of the specific heat capacity versus temperature.]]
-The '''Lambda point''' is the [[temperature]] below which normal fluid [[helium]] (helium I) transitions to [[superfluid]] helium II (approximately 2.17 [[Kelvin|K]]) at 1 [[atmosphere (unit)|atmosphere]].  The lowest pressure lambda point is at 2.172 K, 0.0497 [[atmosphere (unit)|atm]] and highest pressure to achieve superfluidity, the "upper point", is at 1.76 K, 29.8 atm.<ref>http://web.archive.org/web/20070405010647/http://www.fluidmech.net/msc/super/super-f.htm</ref>
+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 (unit)|atmosphere]], the transition occurs at approximately 2.17 [[Kelvin|K]]. The lowest pressure at which He-I and He-II can coexist is the vapor−He-I−He-II [[triple point]] at {{convert|2.1768|K|C}} and {{convert|5.0418|kPa|atm|abbr=on}}, which is the "saturated [[vapor pressure]]" at that temperature (pure helium gas in thermal equilibrium over the liquid surface, in a [[Hermetic seal|hermetic]] container).<ref name=Donnelly>{{cite journal| title=The Observed Properties of Liquid Helium at the Saturated Vapor Pressure | first1=Russell J.| last1=Donnelly| first2=Carlo F.| last2=Barenghi | journal=[[Journal of Physical and Chemical Reference Data]]| year=1998| volume=27| issue=6| pages=1217–1274| doi=10.1063/1.556028|bibcode = 1998JPCRD..27.1217D }}</ref> The highest pressure at which He-I and He-II can coexist is the [[Body-centered cubic|bcc]]−He-I−He-II triple point with a helium solid at {{convert|1.762|K|C}}, {{convert|29.725|atm|kPa|abbr=on}}.<ref name=Hoffer>{{cite journal| title=Thermodynamic properties of <sup>4</sup>He. II. The bcc phase and the P-T and VT phase diagrams below 2 K | first1=J. K.| last1=Hoffer| first2=W. R.| last2=Gardner| first3=C. G.| last3=Waterfield| first4=N. E.| last4=Phillips| journal=[[Journal of Low Temperature Physics]]| date=April 1976| volume=23| issue=1| pages=63–102| doi=10.1007/BF00117245|bibcode = 1976JLTP...23...63H | s2cid=120473493}}</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), which resembles the [[Greek language|Greek]] letter [[lambda]]. The specific heat capacity tends towards [[infinity]] as the temperature approaches the lambda point.
+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 language|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&nbsp;nK below the transition in an experiment included in a [[Space Shuttle]] payload in 1992.<ref name=JPL>{{cite journal| title=Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point | first1=J.A.| last1=Lipa| first2=D. R.| last2=Swanson| first3=J. A.| last3=Nissen| first4=T. C. P.| last4=Chui| first5=U. E.| last5=Israelsson| journal=[[Physical Review Letters]]| year=1996| volume=76| issue=6| pages=944–7| doi=10.1103/PhysRevLett.76.944|bibcode = 1996PhRvL..76..944L| pmid=10061591| hdl=2060/19950007794| s2cid=29876364| hdl-access=free}}</ref>{{unsolved|physics|Explain the discrepancy between the experimental and theoretical determinations of the heat capacity critical exponent {{math|''α''}} for the superfluid transition in helium-4.<ref name="Rychkov"/>
+}}
+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 {{math|''α''}} is the [[critical exponent]]: <math>\alpha=-0.0127(3)</math>.<ref name=JPL /><ref>{{Cite journal|last1=Lipa|first1=J. A.|last2=Nissen|first2=J. A.|last3=Stricker|first3=D. A.|last4=Swanson|first4=D. R.|last5=Chui|first5=T. C. P.|date=2003-11-14|title=Specific heat of liquid helium in zero gravity very near the lambda point|journal=Physical Review B|volume=68|issue=17|pages=174518|doi=10.1103/PhysRevB.68.174518|bibcode=2003PhRvB..68q4518L|arxiv=cond-mat/0310163|s2cid=55646571}}</ref> Since this exponent is negative for the superfluid transition, specific heat remains finite.<ref>For other phase transitions <math>\alpha</math> may be negative (e.g. <math>\alpha\approx+0.1</math> for [[Critical point (thermodynamics)|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 {{math|''α''}} is in a significant disagreement<ref>{{Cite book|last=Vicari|first=Ettore|chapter=Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories |date=2008-03-21|title=Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007)|volume=42|language=en|location=Regensburg, Germany|publisher=Sissa Medialab|pages=023|doi=10.22323/1.042.0023|doi-access=free}}</ref><ref name="Rychkov">{{Cite journal|last=Rychkov|first=Slava|date=2020-01-31|title=Conformal bootstrap and the λ-point specific heat experimental anomaly|url=https://www.condmatjclub.org/?p=4037|journal=Journal Club for Condensed Matter Physics|language=en|doi=10.36471/JCCM_January_2020_02|doi-access=free}}</ref> with the most precise theoretical determinations<ref>{{Cite journal|last1=Campostrini|first1=Massimo|last2=Hasenbusch|first2=Martin|last3=Pelissetto|first3=Andrea|last4=Vicari|first4=Ettore|date=2006-10-06|title=Theoretical estimates of the critical exponents of the superfluid transition in $^{4}\mathrm{He}$ by lattice methods|journal=Physical Review B|volume=74|issue=14|pages=144506|doi=10.1103/PhysRevB.74.144506|arxiv=cond-mat/0605083|s2cid=118924734}}</ref><ref>{{Cite journal|last=Hasenbusch|first=Martin|date=2019-12-26|title=Monte Carlo study of an improved clock model in three dimensions|arxiv=1910.05916|journal=Physical Review B|volume=100|issue=22|pages=224517|doi=10.1103/PhysRevB.100.224517|issn=2469-9950|bibcode=2019PhRvB.100v4517H|s2cid=204509042}}</ref><ref>{{cite journal|last1=Chester|first1=Shai M.|last2=Landry|first2=Walter|last3=Liu|first3=Junyu|last4=Poland|first4=David|last5=Simmons-Duffin|first5=David|last6=Su|first6=Ning|last7=Vichi|first7=Alessandro|title=Carving out OPE space and precise O(2) model critical exponents|journal=Journal of High Energy Physics|year=2020|volume=2020|issue=6|page=142|doi=10.1007/JHEP06(2020)142|arxiv=1912.03324|bibcode=2020JHEP...06..142C|s2cid=208910721}}</ref> coming from high temperature expansion techniques, [[Monte Carlo method|Monte Carlo]] methods and the [[conformal bootstrap]].
 == See also ==
@@ Line 11: / Line 17: @@
 == External links ==
-* [http://www.egglescliffe.org.uk/physics/supercond/supfluid/superfluids.html What is superfluidity?] (includes a graph)
+* [https://web.archive.org/web/20130927063921/http://www.egglescliffe.org.uk/physics/supercond/supfluid/superfluids.html What is superfluidity?]
 {{states of matter}}
+[[Category:Threshold temperatures]]
-{{condensedmatter-stub}}
+[[Category:Superfluidity]]
-[[Category:Temperature]]
+[[Category:Liquid helium]]
-[[ar:نقطة لامدا]]
-[[bs:Lambda tačka]]
-[[de:Lambdapunkt]]
-[[es:Punto lambda]]
-[[eu:Lambda puntu]]
-[[hy:Լամբդա կետ]]
-[[la:Punctum Lambda]]
-[[pl:Przemiana lambda]]
-[[pt:Ponto lambda]]
-[[ru:Лямбда-точка]]

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