Λらむだ点てん

λらむだ點てん是これ氦從したがえ一般いっぱん流體りゅうたい氦(I)相變あいかわ到いた超ちょう流體りゅうたい氦(II)的てき溫度おんど，在ざい1标准大だい气压下した約やく為ため2.17 K。氦（I）和かず氦（II）可か以共存きょうぞん的てき最低さいてい壓力あつりょく是ぜ在ざいHe氣體きたい−He(I)−He(II)的てき三さん相そう点てん，是ぜ在ざい2.1768 K（−270.9732 °C）及5.048 kPa（0.04982 atm），是ぜ該溫度おんど下か的てき飽和ほうわ蒸氣じょうき壓あつ（若わか在ざい氣き封ふう（英えい语：Hermetic seal）的てき容器ようき內，純じゅん氦氣會かい在ざい液體えきたい表面ひょうめん形成けいせい熱ねつ平衡へいこう）^[1]。氦(I)和かず氦(II)可か以共存きょうぞん的てき最高さいこう壓力あつりょく是ぜ立方りっぽう晶あきら系けい氦固體たい−He(I)−He(II)的てき三さん相そう点てん，位い在ざい1.762 K（−271.388 °C）, 29.725 atm（3,011.9 kPa）^[2]。

λらむだ點てん的てき名稱めいしょう是ぜ因いん為ため在ざい上述じょうじゅつ溫度おんど範圍はんい內描繪え比熱ひねつ容よう和わ溫度おんど的まと圖ず時じ（在ざい上述じょうじゅつ的てき壓力あつりょく下か，例れい如一大氣たいき壓力あつりょく），會かい出現しゅつげん希まれ腊文的てき字母じぼλらむだ。當とう溫度おんど接近せっきんλらむだ點てん時じ，其比熱ねつ容よう會かい到達とうたつ其峰值，只ただ有ゆう在ざい零れい重力じゅうりょく時じ才能さいのう準じゅん確かく量りょう測はか到いた可か以說明せつめい比熱ひねつ容よう發散はっさん的てき臨界りんかい指數しすう（為ため了りょう要よう讓ゆずる流體りゅうたい在ざい一體積內的密度是均勻的）。曾在1992年ねん太ふとし空そら船せん的てき酬むくい載の中ちゅう量りょう過か比ひλらむだ點てん低てい2 nK時じ的てき熱ねつ容よう^[3]。

未み解決かいけつ的てき物理ぶつり問題もんだい：說明せつめいHe-4在ざい超ちょう流體りゅうたい形がた變へん時じ熱ねつ容よう臨界りんかい指數しすう

α あるふぁ

理論りろん值和實際じっさい值之間あいだ的てき差異さい原因げんいん^[4]

熱ねつ容よう的てき圖上ずじょう有ゆう出現しゅつげん峰ほう值，而附近ふきん的てき斜はす率りつ很大，但ただし在ざい該點的てき值不會かい趨近無限むげん大だい，在ざい形かたち變へん點てん前後ぜんこう的てき值都是ぜ有限ゆうげん值^[3]。熱ねつ容よう在ざい峰みね值附近ふきん的てき行為こうい可か以用 $C\approx A_{\pm }t^{-\alpha }+B_{\pm }$ 公式こうしき表示ひょうじ，其中 $t=|1-T/T_{c}|$ 是ぜ對比たいひ溫度おんど（reduced temperature）， $T_{c}$ 是ぜΛらむだ点てん溫度おんど， $A_{\pm },B_{\pm }$ 是ぜ常數じょうすう（在ざい形かたち變へん點前てまえ和わ形がた變へん點てん後ご各かく有ゆう一いち組くみ值）， $α あるふぁ$ 為ため临界指数しすう： $\alpha =-0.0127(3)$ ^[3]^[5]。因よし為ため在ざい超ちょう流體りゅうたい相しょう變へん時じ，該指數すう為ため負まけ，因いん此比熱ねつ仍為有限ゆうげん值

临界指数しすう $α あるふぁ$ 的てき實際じっさい值和最さい精せい準じゅん的てき理論りろん判定はんてい技術ぎじゅつ所得しょとく值之間あいだ，仍有很大的てき差異さい^[6]^[4]，這些技術ぎじゅつ^[7]^[8]^[9]包括ほうかつ高溫こうおん膨脹ぼうちょう技術ぎじゅつ、蒙こうむ地ち卡羅方法ほうほう以及Conformal bootstrapping（英えい语：Conformal bootstrapping）。

參考さんこう資料しりょう

^ Donnelly, Russell J.; Barenghi, Carlo F. The Observed Properties of Liquid Helium at the Saturated Vapor Pressure. Journal of Physical and Chemical Reference Data. 1998, 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. Thermodynamic properties of ⁴He. II. The bcc phase and the P-T and VT phase diagrams below 2 K. Journal of Low Temperature Physics. April 1976, 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245.
^ ^3.0 ^3.1 ^3.2 Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point. Physical Review Letters. 1996, 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944.
^ ^4.0 ^4.1 Rychkov, Slava. Conformal bootstrap and the λらむだ-point specific heat experimental anomaly. Journal Club for Condensed Matter Physics. 2020-01-31 [2024-01-22]. doi:10.36471/JCCM_January_2020_02 . （原始げんし内容ないよう存そん档于2020-06-09）（英えい语）.
^ Lipa, J. A.; Nissen, J. A.; Stricker, D. A.; Swanson, D. R.; Chui, T. C. P. Specific heat of liquid helium in zero gravity very near the lambda point. Physical Review B. 2003-11-14, 68 (17): 174518. Bibcode:2003PhRvB..68q4518L. S2CID 55646571. arXiv:cond-mat/0310163 . doi:10.1103/PhysRevB.68.174518.
^ Vicari, Ettore. Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories. Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007) (Regensburg, Germany: Sissa Medialab). 2008-03-21, 42: 023. doi:10.22323/1.042.0023  （英えい语）.
^ Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore. Theoretical estimates of the critical exponents of the superfluid transition in $^{4}\mathrm{He}$ by lattice methods. Physical Review B. 2006-10-06, 74 (14): 144506. S2CID 118924734. arXiv:cond-mat/0605083 . doi:10.1103/PhysRevB.74.144506.
^ Hasenbusch, Martin. Monte Carlo study of an improved clock model in three dimensions. Physical Review B. 2019-12-26, 100 (22): 224517. Bibcode:2019PhRvB.100v4517H. ISSN 2469-9950. S2CID 204509042. arXiv:1910.05916 . doi:10.1103/PhysRevB.100.224517.
^ Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro. Carving out OPE space and precise O(2) model critical exponents. Journal of High Energy Physics. 2020, 2020 (6): 142. Bibcode:2020JHEP...06..142C. S2CID 208910721. arXiv:1912.03324 . doi:10.1007/JHEP06(2020)142.

外部がいぶ連結れんけつ

What is superfluidity?

[Donnelly-1] Donnelly, Russell J.; Barenghi, Carlo F. The Observed Properties of Liquid Helium at the Saturated Vapor Pressure. Journal of Physical and Chemical Reference Data. 1998, 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. Thermodynamic properties of ⁴He. II. The bcc phase and the P-T and VT phase diagrams below 2 K. Journal of Low Temperature Physics. April 1976, 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245.

[JPL-3] 3.0 ^3.1 ^3.2 Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point. Physical Review Letters. 1996, 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944.

[Rychkov-4] 4.0 ^4.1 Rychkov, Slava. Conformal bootstrap and the λらむだ-point specific heat experimental anomaly. Journal Club for Condensed Matter Physics. 2020-01-31 [2024-01-22]. doi:10.36471/JCCM_January_2020_02 . （原始げんし内容ないよう存そん档于2020-06-09）（英えい语）.

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

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

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

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

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

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參考さんこう資料しりょう

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