Skip to main content
Log in

From Thermodynamically Driven Phase Transitions to Quantum Critical Phenomena

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

In this short review some basic concepts of phase transitions at non-zero and zero temperature are highlighted. For that the critical behavior of classical, thermodynamically driven magnetic phase transitions is exemplified for conventional universality classes as well as for systems reflecting chiral order. Finally the quantum critical phenomena for two magnetic-field-driven phase transitions are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Landau L.D. Phys. Z. Sowjetunion 11, 26 (1937); ibid. 11, 545 (1937).

  2. W. Gebhardt, Krey U., Phasenübergänge und kritische Phänomene Vieweg, Braunschweig/Wiesbaden, 1980.

  3. Lang M. (1996) Supercond. Rev. 2: 1

    Google Scholar 

  4. Wilson K.G. Phys. Rev. B 4, 3174 (1971); ibid. 3184 (1971).

  5. Kadanoff L.P. Nuovo Cimento 44, 276 (1966); Physics 2, 263 (1966).

  6. A. Pelissetto, Vicari E. (2002) Phys. Rep. 368:549

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Kawamura H., J. Phys.: Condens. Matter 10, 4707 (1998); Kawamura H., Can. J. Phys. 79, 1447 (2001).

  8. Kawamura H., J. Phys. Soc. Jpn. 54, 3220 (1985); Kawamura H., J. Phys. Soc. Jpn. 55, 2095 (1986).

  9. Azaria P., Delamotte B., Th. Jolicoeur, Phys. Rev. Lett. 64, 3175 (1990); Azaria P., Delamotte B., Delduc F., Th. Jolicoeur, Nucl. Phys. B 408, 485 (1993).

  10. Antonenko S.A., Sokolov A.I. (1994) Phys. Rev. B 49(15):901

    Google Scholar 

  11. D. Loison, Schotte K.D. Eur. Phys. J. B 5, 735 (1998); D. Loison, Schotte K.D. Eur. Phys. J. B 14, 125 (2000); Kanki K., Loison D., Schotte K.D. J. Phys. Soc. Jpn. 75, 015001 (2006).

  12. Tissier M., Delamotte B., Mouhanna D. (2000) Phys. Rev. Lett. 84: 5208

    Article  ADS  Google Scholar 

  13. Kanki K., Loison D., Schotte K.D. (2006) J. Phys. Soc. Jpn. 75:015001

    Article  ADS  Google Scholar 

  14. Loison D., Diep. . Phys. Rev. B 50 (1994).

  15. Mailhot A., Plumer M.L., A. Caillé (1994) Phys. Rev. B 50:6854

    Article  ADS  Google Scholar 

  16. Pelissetto A., Rossi P., Vicari E. (2001) Phys. Rev. B 63:140414(R)

    Article  ADS  Google Scholar 

  17. Pelissetto A., Rossi P., Vicari E. (2002) Phys. Rev. B 65, 020403(R)

    ADS  Google Scholar 

  18. Delamotte B., Mouhanna D., Tissier M. (2004) Phys. Rev. B 69:134413

    Article  ADS  Google Scholar 

  19. Kornblit A., Ahlers G. (1973) Phys. Rev. B 8:5163

    Article  ADS  Google Scholar 

  20. Introducing α in the denominator of the first term in (2) helps to stabilize the numerical fit procedure for α close to zero.

  21. Lipa J.A., Swanson D.R., Nissen J.A., Chui T.C.P., Israelsson U.E. (1996) Phys. Rev. Lett. 76:944

    Article  ADS  Google Scholar 

  22. J. Wosnitza, Löhneysen H.v., Europhys. Lett. 10, 381 (1989); J. de Physique Coll. 49, C8-1203 (1988).

  23. Stroka B., Wosnitza J., Scheer E., Löhneysen H.v., Park W., Fischer K., (1992) Z. Phys. B 89:39

    Article  Google Scholar 

  24. A. Kornblit, Ahlers G., Phys. Rev. B 11, 2678 (1975); Kornblit A., Ahlers G., E. Bühler, Phys. Lett. A 43, 531 (1973).

  25. Scheer E., Wosnitza J., Löhneysen H.v., Z. Phys. B 85, 79 (1991); Scheer E., Wosnitza J., Löhneysen H.v., R. Kürsch, Lang M., Steglich F., J. Magn. Magn. Mat. 104–107, 175 (1992).

    Google Scholar 

  26. Löhneysen H.v.,Beckmann D., Wosnitza J., Visser D. (1995) J. Magn. Magn. Mat. 140–144: 1469

    Article  ADS  Google Scholar 

  27. Weber H., Beckmann D., Wosnitza J., Löhneysen H.v., Visser D. (1995) Int. J. Mod. Phys. B 9: 1387

    Article  ADS  Google Scholar 

  28. Falk U., Furrer A., Güdel H.U., Kjems J.K. (1987) Phys. Rev. B 35:4888

    Article  ADS  Google Scholar 

  29. Ajiro Y., Nakashima T., Unno Y., Kadowaki H., Mekata M., Achiwa N., J. Phys. Soc. Jpn. 57, 2648 (1988); Kadowaki H., Shapiro S.M., Inami T., Ajiro Y., J. Phys. Soc. Jpn. 57, 2640 (1988).

    Google Scholar 

  30. Mason T.E., Gaulin B.D., Collins M.F. (1989) Phys. Rev. B 39:586

    Article  ADS  Google Scholar 

  31. Wang J., Belanger D.P., Gaulin B.D. (1991) Phys. Rev. Lett. 66:3195

    Article  ADS  Google Scholar 

  32. Deutschmann R., Löhneysen H.v., Wosnitza J., Kremer R.K., Visser D. (1992) Europhys. Lett. 17:637

    ADS  Google Scholar 

  33. Gaulin B.D., Mason T.E., Collins M.F., Larese J.Z. (1989) Phys. Rev. Lett. 62:1380

    Article  ADS  Google Scholar 

  34. Kawamura H., Caillé A., Plumer M.L. (1990) Phys. Rev. B 41:4416

    Article  ADS  Google Scholar 

  35. Goto T., Inami T., Ajiro Y. (1990) J. Phys. Soc. Jpn. 59:2328

    Article  Google Scholar 

  36. Yamada I., Ubukoshi K., Hirakawa K. (1984) J. Phys. Soc. Jpn. 53:381

    Article  Google Scholar 

  37. Collins M.F., Petrenko O.A. (1997) Can. J. Phys. 75:605

    Article  ADS  Google Scholar 

  38. Kadowaki H., Ubukoshi K., Hirakawa K., Martinez J.L., Shirane G. (1987) J. Phys. Soc. Jpn. 56:4027

    Article  Google Scholar 

  39. Wosnitza J., Deutschmann R., Löhneysen H.v., Kremer R.K. (1994) J. Phys.: Cond. Matter 6:8045

    Article  ADS  Google Scholar 

  40. Takeda K., Uryû N., Ubukoshi K., Hinkawa K. (1986) J. Phys. Soc. Japan 55:727

    Article  Google Scholar 

  41. Kadowaki H., Inami T., Ajiro Y., Nakajima K., Endoh Y., J. Phys. Soc. Jpn. 60, 1708 (1991); Ajiro Y., Inami T., H. Kadowaki, J. Phys. Soc. Jpn. 59, 4142 (1990); Harrison A., Collins M.F. J. Abu-Dayyeh, Stager C.V. Phys. Rev. B 43, 679 (1991).

  42. Beckmann D., Wosnitza J., Löhneysen H.v., Visser D. (1993) Phys. Rev. Lett. 71:2829

    Article  ADS  Google Scholar 

  43. Beckmann D., Wosnitza J., Löhneysen H.v., Visser D. (1993) J. Phys.: Cond. Matter 5:6289

    Article  ADS  Google Scholar 

  44. Plumer M.L., Caillé A. (1990) Phys. Rev. B 41:2543

    Article  ADS  Google Scholar 

  45. Johnson P.B. Rayne J.A., Friedberg S.A. (1979) J. Appl. Phys. 50:1853

    Article  ADS  Google Scholar 

  46. Poirier M., Caillé A., Plumer M.L. (1990) Phys. Rev. B 41:4869

    Article  ADS  Google Scholar 

  47. Enderle M., Furkuma G., Steiner M. (1994) J. Phys.: Cond. Matter. 27:385

    Article  Google Scholar 

  48. Quirion G., Han X., Plumer M.L., Poirier M. (2006) Phys. Rev. Lett. 97:077202

    Article  ADS  Google Scholar 

  49. Adachi K., Achiwa N., Mekata M. (1980) J. Phys. Soc. Jpn. 49:545

    Article  Google Scholar 

  50. Mino M., Ubukata K., Bokui T., Arai M., Tanaka H., Motokawa M. (1994) Physica B 201:213

    Article  ADS  Google Scholar 

  51. Nikuni T., Shiba H. (1993) J. Phys. Soc. Jpn. 62:3268

    Article  Google Scholar 

  52. Werner T., Weber H.B. Wosnitza J., Kelnberger A., Meschke M., Schotte U., N. Stüßer, Ding Y., Winkelmann M., Solid State Commun. 102, 609 (1997); R. Bügel, A. Faißt, Löhneysen H.v., Wosnitza J., Schotte U., Phys. Rev. B 65, 052402 (2001).

  53. Stüßer N., Schotte U., Hoser A., Meschke M., Meißner M., Wosnitza J. (2002) J. Phys.: Condens. Matter 14:5161

    Article  ADS  Google Scholar 

  54. Weber H.B. Werner T., Wosnitza J., Löhneysen H.v., Schotte U. (1996) Phys. Rev. B 54(15):924

    Google Scholar 

  55. Wada J.N. Ubukoshi K., Hirakawa K. (1982) J. Phys. Soc. Jpn. 51:2833

    Article  Google Scholar 

  56. Mekata M., Ajiro Y., Sugino T., Oohara A., Ohara K., Yasuda S., Oohara Y., Yoshizawa H. (1995) J. Magn. Magn. Mat. 140–144: 1987

    Article  ADS  Google Scholar 

  57. Plakhty V.P. Regnault L.P., Wosnitza J., unpublished results.

  58. Maleyev S.V. (1995) Phys. Rev. Lett. 75:4682

    Article  ADS  Google Scholar 

  59. Maleyev S.V., Plakhty V.P., Smirnov O.P., Wosnitza J., Visser D., Kremer R.K., Kulda J. (1998) J. Phys.: Condens. Matter 10:951

    Article  ADS  Google Scholar 

  60. Plakhty V.P. Maleyev S.V. Kulda J., Wosnitza J., Visser D., Moskvin E. (1999) Europhys. Lett. 48:215

    Article  ADS  Google Scholar 

  61. Mason T.E., Yang Y.S., Collins M.F., Gaulin B.D., Clausen K.N., Harrison A.(1992) J. Magn. Mag. Mat. 104–107:197

    Article  ADS  Google Scholar 

  62. Plakhty V.P., Kulda J., Visser D., Moskvin E.V., Wosnitza J. (2000) Phys. Rev. Lett. 85:3942

    Article  ADS  Google Scholar 

  63. Maleyev S.V., Bar’yahtar V.G., Suris R.A. (1963) Sov. Phys. Solid State 4:2533

    Google Scholar 

  64. Blume M. (1963) Phys. Rev. 130:1670

    Article  ADS  Google Scholar 

  65. Tasset F., Brown P.J., Forsyth J.B. J. Appl. Phys. 63, 3606 (1988); Brown P.J. Nunez V., Tasset F., Forsyth J.B. and Radhakrishna P., J. Phys.: Condens. Matter 2, 9409 (1990); Fiebig M., D. Fröhlich, Leute S., Pisarev R.V. J. Appl. Phys. 83, 6560 (1998).

  66. P. Bak, Mukamel D. (1976) Phys. Rev. B 13:5086

    Article  ADS  Google Scholar 

  67. Kawamura H. (1992) J. Phys. Soc. Jpn. 61:1299

    Article  Google Scholar 

  68. Kawamura H., Phys. Rev. B 38, 4916 (1988); J. Phys. Soc. Jpn. 59, 2305 (1990).

    Google Scholar 

  69. Coleman P. (2001) Nature 413:788

    Article  ADS  Google Scholar 

  70. Sachdev S. (2000) Science 288:475

    Article  ADS  Google Scholar 

  71. S. Sachdev, Starykh O.A. Nature 405, 322 (2000); Waffenschmidt S., Pfleiderer C., Löhneysen H.v., Phys. Rev. Lett. 83, 3005 (1999), references therein.

  72. M. Fisher P.A. Phys. Rev. Lett. 65, 923 (1990); A. F. Hebard and Paalanen M.A.ibid. 927.

  73. Mason N., Kapitulnik A. (1999) Phys. Rev. Lett. 82:5341

    Article  ADS  Google Scholar 

  74. Marković N., Christiansen C., Mack A.M. Huber W.H., Goldman A.M. (1999) Phys. Rev. B 60:4320

    Article  ADS  Google Scholar 

  75. Wanka S., Hagel J., Beckmann D., Wosnitza J., Schlueter J.A., Williams J.M., Nixon P.G., Winter R.W., Gard G.L. (1998) Phys. Rev. B 57:3084

    Article  ADS  Google Scholar 

  76. Wosnitza J., Goll G., Beckmann D., Wanka S., Schlueter J.A., Williams J.M., Nixon P.G., Winter R.W., Gard G.L. (1998) Physica B 246–247:104

    Article  ADS  Google Scholar 

  77. Wosnitza J., Wanka S., Hagel J., Balthes E., Harrison N., Schlueter J.A. Kini A.M. Geiser U., Mohtasham J., Winter R.W., Gard G.L. (2000) Phys. Rev. B 61:7383

    Article  ADS  Google Scholar 

  78. Beckmann D., Wanka S., Wosnitza J., Schlueter J.A. Williams J.M., Nixon P.G., Winter R.W., Gard G.L., Ren J., Whangbo M.-H. (1998) Eur. Phys. J. B 1:295

    Article  ADS  Google Scholar 

  79. Wosnitza J., Wanka S., Qualls J.S., Brooks J.S., Mielke C.H., Harrison N., Schlueter J.A., Williams J.M., Nixon P.G., Winter R.W., Gard G.L. (1999) Synth. Met. 103:2000

    Article  Google Scholar 

  80. Wosnitza J., Hagel J., Qualls J.S., Brooks J.S., Balthes E., Schweitzer D., Schlueter J.A., Geiser U., Mohtasham J., Winter R.W. Gard G.L. (2002) Phys. Rev. B 65:180506(R)

    Article  ADS  Google Scholar 

  81. Wosnitza J., Hagel J., Ignatchik O., Bergk B., Gvozdikov V.M., Schlueter J.A., Winter R.W., Gard G.L. (2006) J. Low Temp. Phys. 142, 327

    Google Scholar 

  82. McKenzie R.H., Moses P., Phys. Rev. Lett. 81, 4492 (1998); P. Moses, McKenzie R.H. Phys. Rev. B 60, 7998 (1999).

  83. Maple M.B. Bauer E.D. Zapf V.S., Wosnitza J., in The Physics of Superconductors Vol. II, eds. K. H. Bennemann and J. B. Ketterson (Springer-Verlag, Berlin, 2004).

  84. Wosnitza J., Hagel J., Meeson P.J. Bintley D., Schlueter J.A., Mohtasham J., Winter R.W., Gard G.L. (2003) Phys. Rev. B 67:060504(R)

    Article  ADS  Google Scholar 

  85. V. M. Gvozdikov, Wosnitza J., Physica B 359-361, 614 (2005); Low. Temp. Phys. 32, 152 (2006)

    Google Scholar 

  86. Wosnitza J., Wanka S., Hagel J., Löhneysen H.v., Qualls J.S., Brooks J.S., Balthes E., Schlueter J.A., Geiser U., Mohtasham J., Winter R.W., Gard G.L. (2001) Phys. Rev. Lett. 86:508

    Article  ADS  Google Scholar 

  87. McKenzie R.H., Qualls J.S., Han S.Y., Brooks J.S. (1998) Phys. Rev. B 57(11): 854

    Google Scholar 

  88. Zuo F., Su X., Zhang P., Brooks J.S., Wosnitza J., Schlueter J.A., Williams J.M., Nixon P.G., Winter R.W., Gard G.L. (1999) . Phys. Rev. B 60: 6296

    Article  ADS  Google Scholar 

  89. Lifshitz I.M. (1969) Zh. Eksp. Teor. Fiz. 38:1569

    Google Scholar 

  90. Kozlova N., Hagel J., Doerr M., Wosnitza J., Eckert D., Müller K.-H., Schultz L., Opahle I., Elgazzar S., Richter M., Goll G., Löhneysen H.v., Zwicknagl G., Yoshino T., Takabatake T. (2005) Phys. Rev. Lett. 95:086403

    Article  ADS  Google Scholar 

  91. Wosnitza J., Goll G., Bianchi A.D. Bergk B., Kozlova N., Opahle I., Elgazzar S., Richter M., Stockert O., Löhneysen H.v., Yoshino T., Takabatake T. (2006) New J. Phys. 8:174

    Article  ADS  Google Scholar 

  92. Pietrus T., Mioković T., Schröder A., Löhneysen H.v., Yoshino T., Takagi K., Umeo K., Takabatake T. (2000) Physica B 281–282:745

    Article  ADS  Google Scholar 

  93. Goll G., Hagel J., Löhneysen H.v., Pietrus T., Wanka S., Wosnitza J., Zwicknagl G., Yoshino T., Takabatake T. (2002) Europhys. Lett. 57:233

    Article  ADS  Google Scholar 

  94. Wosnitza J., Hagel J., Kozlova N., Eckert D., Müller K.-H., Mielke C.H., Goll G., Yoshino T., Takabatake T. (2004) Physica B 346–347:127

    Article  ADS  Google Scholar 

  95. Shoenberg D. (1984) Magnetic Oscillations in Metals. Cambridge University Press, Cambridge

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Wosnitza.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wosnitza, J. From Thermodynamically Driven Phase Transitions to Quantum Critical Phenomena. J Low Temp Phys 147, 249–278 (2007). https://doi.org/10.1007/s10909-007-9309-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-007-9309-x

PACS Numbers

Navigation