Phases and phase transitions in disordered quantum systems

AIP Conference Proceedings

Volumn 1550, Issue , 2013, Pages 188-247

  Vojta, Thomas ^a  

^a MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

Author keywords

critical point; disorder; Griffiths singularity; phase transition; renormalization group

Indexed keywords

EID: 84884196775     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.4818403     Document Type: Conference Paper

References (120)

1. T. Vojta, J. Phys. A 39, R143 (2006).
2. T. Vojta, J. Low Temp. Phys. 161, 299 (2010).
3. F. Igloi, and C. Monthus, Phys. Rep. 412, 277 (2005).
4. N. Goldenfeld, Lectures on phase transitions and the renormalization group, Addison-Wesley, Reading, 1992.
5. S. Sachdev, Quantum phase transitions, Cambridge University Press, Cambridge, 1999.
6. P. Ehrenfest, Proc. Kon. Ned. Akad. Wet. (Amsterdam) 36, 153 (1933).
7. T. Andrews, Phil. Trans. R. Soc. 159, 575 (1869).
8. M. de Podesta, Critical opalescence (2013), http://www.physicsofmatter. com/.
9. R. Swendsen, and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987).
10. U. Wolff, Phys. Rev. Lett. 62, 361 (1989).
11. B. Widom, J. Chem. Phys. 43, 3892 (1965).
12. K. G. Wilson, and J. Kogut, Phys. Rep. 12, 75 (1974).
13. L. D. Landau, Phys. Z. Sowjetunion 11, 26 (1937).
14. L. D. Landau, Zh. Eksp. Teor. Fiz. 7, 19 (1937).
15. L. D. Landau, Phys. Z. Sowjetunion 11, 545 (1937).
16. L. D. Landau, Zh. Eksp. Teor. Fiz. 7, 627 (1937).
17. F. Alet, A. M. Walczak, and M. P. A. Fisher, Physica A 369, 122 (2006).
18. S. Sachdev (2009), arXiv:0901.4103.
19. D. Bitko, T. F. Rosenbaum, and G. Aeppli, Phys. Rev. Lett. 77, 940 (1996).
20. L. Demkó, S. Bordács, T. Vojta, D. Nozadze, F. Hrahsheh, C. Svoboda, B. Dóra, H. Yamada, M. Kawasaki, Y. Tokura, and I. Kézsmárki, Phys. Rev. Lett. 108, 185701 (2012).
21. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
22. H. F. Trotter, Proc. American Math. Soc. 10, 545 (1959).
23. R. P. Feynman, and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965.
24. S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997).
25. M. N. Barber, "Finite-Size Scaling," in Phase Transitions and Critical Phenomena, edited by C. Domb, and J. L. Lebowitz, Academic, New York, 1983, vol. 8, pp. 145-266.
26. T. Vojta, D. Belitz, R. Narayanan, and T. R. Kirkpatrick, Europhys. Lett. 36, 191 (1996).
27. D. Belitz, T. R. Kirkpatrick, and T. Vojta, Phys. Rev. B 65, 165112 (2002).
28. D. Belitz, T. R. Kirkpatrick, and T. Vojta, Rev. Mod. Phys. 77, 579 (2005).
29. S. F. Edwards, and P. W. Anderson, Journal of Physics F: Metal Physics 5, 965 (1975).
30. K. H. Fischer, and J. A. Hertz, Spin glasses, Cambridge University Press, Cambridge, 1991.
31. A. B. Harris, J. Phys. C 7, 1671 (1974).
32. A. Weinrib, and B. I. Halperin, Phys. Rev. B 27, 413-427 (1983).
33. J. T. Chayes, L. Chayes, D. S. Fisher, and T. Spencer, Phys. Rev. Lett. 57, 2999 (1986).
34. Y. Imry, and S.-k. Ma, Phys. Rev. Lett. 35, 1399-1401 (1975).
35. M. Aizenman, and J. Wehr, Phys. Rev. Lett. 62, 2503 (1989).
36. T. Nattermann, J. Phys. C 16, 6407 (1983).
37. Y. Imry, and M. Wortis, Phys. Rev. B 19, 3580 (1979).
38. K. Hui, and A. N. Berker, Phys. Rev. Lett. 62, 2507 (1989).
39. R. L. Greenblatt, M. Aizenman, and J. L. Lebowitz, Phys. Rev. Lett. 103, 197201 (2009).
40. P. Pfeuty, Phys. Lett. A 72, 245 (1979).
41. R. Narayanan, T. Vojta, D. Belitz, and T. R. Kirkpatrick, Phys. Rev. Lett. 82, 5132 (1999).
42. R. Narayanan, T. Vojta, D. Belitz, and T. R. Kirkpatrick, Phys. Rev. B 60, 10150 (1999).
43. S. K. Ma, C. Dasgupta, and C. K. Hu, Phys. Rev. Lett. 43, 1434 (1979).
44. D. S. Fisher, Phys. Rev. Lett. 69, 534 (1992).
45. D. S. Fisher, Phys. Rev. B 50, 3799 (1994).
46. D. S. Fisher, Phys. Rev. B 51, 6411 (1995).
47. R. B. Griffiths, Phys. Rev. Lett. 23, 17 (1969).
48. M. Wortis, Phys. Rev. B 10, 4665 (1974).
49. A. B. Harris, Phys. Rev. B 12, 203 (1975).
50. Y. Imry, Phys. Rev. B 15, 4448 (1977).
51. A. J. Bray, and D. Huifang, Phys. Rev. B 40, 6980 (1989).
52. P. C. Hohenberg, and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).
53. R. J. Glauber, J. Math. Phys. 4, 294 (1963).
54. N. Metropolis, A. Rosenbluth, M. Rosenbluth, and A. Teller, J. Chem. Phys. 21, 1087 (1953).
55. D. Dhar, "Stochastic evolution in Ising models," in Stochastic Processes: Formalism and Applications, edited by D. S. Argawal, and S. Dattagupta, Springer, Berlin, 1983, p. 300.
56. M. Randeria, J. P. Sethna, and R. G. Palmer, Phys. Rev. Lett. 54, 1321 (1985).
57. A. J. Bray, Phys. Rev. Lett. 60, 720 (1988).
58. A. J. Bray, J. Phys. A. 22, L81 (1989).
59. T. Senthil, and S. Sachdev, Phys. Rev. Lett. 77, 5292 (1996).
60. T. Vojta, and J. A. Hoyos, "Quantum phase transitions on percolating lattices," in Recent Progress in Many-Body Theories, edited by J. Boronat, G. Astrakharchik, and F. Mazzanti, World Scientific, Singapore, 2008, p. 235.
61. B. M. McCoy, and T. T. Wu, Phys. Rev. Lett. 21, 549 (1968).
62. B. M. McCoy, and T. T. Wu, Phys. Rev. 176, 631 (1968).
63. B. M. McCoy, and T. T. Wu, Phys. Rev. 188, 982 (1969).
64. M. Thill, and D. A. Huse, Physica A 214, 321 (1995).
65. M. Guo, R. N. Bhatt, and D. A. Huse, Phys. Rev. B 54, 3336 (1996).
66. H. Rieger, and A. P. Young, Phys. Rev. B 54, 3328 (1996).
67. A. P. Young, and H. Rieger, Phys. Rev. B 53, 8486 (1996).
68. T. Vojta, and J. Schmalian, Phys. Rev. B 72, 045438 (2005).
69. H. G. Ballesteros, L. A. Fernandez, V. Martin-Mayor, A. Munoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo, Phys. Rev. B 58, 2740 (1998).
70. R. Sknepnek, T. Vojta, and M. Vojta, Phys. Rev. Lett. 93, 097201 (2004).
71. J. Hooyberghs, F. Igloi, and C. Vanderzande, Phys. Rev. Lett. 90, 100601 (2003).
72. T. Vojta, J. Phys. A 36, 10921 (2003).
73. T. Vojta, Phys. Rev. Lett. 90, 107202 (2003).
74. T. Vojta, Phys. Rev. E 70, 026108 (2004).
75. M. Marcellini, M. Pärnaste, B. Hjörvarsson, and M. Wolff, Phys. Rev. B 79, 144426 (2009).
76. I. M. Lifshitz, Usp. Fiz. Nauk 83, 617 (1964), [Sov. Phys.-Usp. 7, 549 (1965)].
77. I. M. Lifshitz, Adv. Phys. 13, 483 (1964).
78. B. I. Halperin, and M. Lax, Phys. Rev. 148, 722 (1966).
79. R. Sknepnek, and T. Vojta, Phys. Rev. B 69, 174410 (2004).
80. F. Hrahsheh, D. Nozadze, and T. Vojta, Phys. Rev. B 83, 224402 (2011).
81. C. Svoboda, D. Nozadze, F. Hrahsheh, and T. Vojta, EPL (Europhysics Letters) 97, 20007 (2012).
82. G. Schehr, and H. Rieger, Phys. Rev. Lett. 96, 227201 (2006).
83. G. Schehr, and H. Rieger, J. Stat. Mech. 2008, P04012 (2008).
84. J. A. Hoyos, and T. Vojta, Phys. Rev. Lett. 100, 240601 (2008).
85. J. A. Hoyos, and T. Vojta, Phys. Rev. B 85, 174403 (2012).
86. A. O. Caldeira, and A. J. Legett, Ann. Phys. (N.Y.) 149, 374 (1983).
87. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
88. U. Weiss, Quantum disspative systems, World Scientific, Singapore, 1993.
89. J. A. Hoyos, and T. Vojta, Phys. Rev. B 74, 140401(R) (2006).
90. J. Hertz, Phys. Rev. B 14, 1165 (1976).
91. A. J. Millis, Phys. Rev. B 48, 7183 (1993).
92. H. von Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007).
93. P. Gegenwart, Q. Si, and F. Steglich, Nature Physics 4, 186 (2008).
94. D. J. Thouless, Phys. Rev. 187, 732 (1969).
95. J. Cardy, J. Phys. A 14, 1407 (1981).
96. A. J. Millis, D. K. Morr, and J. Schmalian, Phys. Rev. Lett. 87, 167202 (2001).
97. A. J. Millis, D. K. Morr, and J. Schmalian, Phys. Rev. B 66, 174433 (2002).
98. A. H. Castro Neto, G. Castilla, and B. A. Jones, Phys. Rev. Lett. 81, 3531 (1998).
99. A. H. Castro Neto, and B. A. Jones, Phys. Rev. B 62, 14975 (2000).
100. G. S. Joyce, J. Phys. C: Solid State Phys. 2, 1531 (1969).
101. F. J. Dyson, Commun. Math. Phys. 12, 91 (1969).
102. P. Bruno, Phys. Rev. Lett. 87, 137203 (2001).
103. D. Nozadze, and T. Vojta, EPL (Europhysics Letters) 95, 57010 (2011).
104. J. A. Hoyos, C. Kotabage, and T. Vojta, Phys. Rev. Lett. 99, 230601 (2007).
105. T. Vojta, C. Kotabage, and J. A. Hoyos, Phys. Rev. B 79, 024401 (2009).
106. V. Dobrosavljevic, and E. Miranda, Phys. Rev. Lett. 94, 187203 (2005).
107. S. Guo, D. P. Young, R. T. Macaluso, D. A. Browne, N. L. Henderson, J. Y. Chan, L. Henry, and J. F. DiTusa, Phys. Rev. Lett. 100, 017209 (2007).
108. S. Guo, D. P. Young, R. T. Macaluso, D. A. Browne, N. L. Henderson, J. Y. Chan, L. L. Henry, and J. F. DiTusa, Phys. Rev. B 81, 144423 (2010).
109. S. Guo, D. P. Young, R. T. Macaluso, D. A. Browne, N. L. Henderson, J. Y. Chan, L. L. Henry, and J. F. DiTusa, Phys. Rev. B 81, 144424 (2010).
110. J. G. Sereni, T. Westerkamp, R. Küchler, N. Caroca-Canales, P. Gegenwart, and C. Geibel, Phys. Rev. B 75, 024432 (2007).
111. T. Westerkamp, M. Deppe, R. Küchler, M. Brando, C. Geibel, P. Gegenwart, A. P. Pikul, and F. Steglich, Phys. Rev. Lett. 102, 206404 (2009).
112. S. Ubaid-Kassis, T. Vojta, and A. Schroeder, Phys. Rev. Lett. 104, 066402 (2010).
113. A. Schroeder, S. Ubaid-Kassis, and T. Vojta, J. Phys. Condes. Matter 23, 094205 (2011).
114. D. Nozadze, and T. Vojta, Phys. Rev. B 85, 174202 (2012).
115. P. Mohan, R. Narayanan, and T. Vojta, Phys. Rev. B 81, 144407 (2010).
116. F. Hrahsheh, H. Barghathi, and T. Vojta, Phys. Rev. B 84, 184202 (2011).
117. P. Mohan, P. M. Goldbart, R. Narayanan, J. Toner, and T. Vojta, Phys. Rev. Lett. 105, 085301 (2010).
118. D. Pekker, G. Refael, and E. Demler, Phys. Rev. Lett. 105, 085302 (2010).
119. O. Motrunich, S. C. Mau, D. A. Huse, and D. S. Fisher, Phys. Rev. B 61, 1160 (2000).
120. R. M. Fernandes, and J. Schmalian, Phys. Rev. Lett. 106, 067004 (2011).