Three-Dimensional Critical Behavior with 2D, 1D, and 0D Dimensionality Crossover: Surface and Edge Specific Heats

Physical Review Letters

Volumn 92, Issue 11, 2004, Pages

  Kimball, M O ^a   Mooney, K P ^a   Gasparini, F M ^a  

^a UNIVERSITY AT BUFFALO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; HELIUM; LITHOGRAPHY; MONTE CARLO METHODS; PHASE TRANSITIONS; SILICON WAFERS; SURFACE PHENOMENA; THERMODYNAMICS; VAN DER WAALS FORCES;

DIRECT WAFER BONDING; EDGE SPECIFIC HEATS; FINITE-SIZE CONFINEMENT; SUPERFLUID TRANSITION; THREE-DIMENSIONAL CRITICAL BEHAVIOR;

SPECIFIC HEAT;

EID: 2342564971     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.92.115301     Document Type: Article

References (22)

1. See, for instance, Shang-Keng Ma, Modern Theory of Critical Phenomena (Benjamin/Cunnings, Reading, MA, 1981).
2. M. E. Fisher, in Critical Phenomena, Proceedings of the 51st "Enrico Fermi" Summer School, Varenna, Italy, edited by M. S. Green (Academic Press, New York, 1971); see also M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).
3. M. E. Fisher, in Critical Phenomena, Proceedings of the 51st "Enrico Fermi" Summer School, Varenna, Italy, edited by M. S. Green (Academic Press, New York, 1971); see also M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).
4. V. Privman, Finite Size Scaling and Numerical Simulations of Statistical Systems (World Scientific, Teaneck, NJ, 1990), see, in particular, Eqs. 2.28 and 2.41-2.42.
5. See, for instance, G. Ahlers, in The Physics of Liquid and Solid Helium, edited by K.H. Bennemann and J.B. Ketterson (J. Wiley, New York, 1976).
6. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973).
7. I. Rhee, D. J. Bishop, A. Petrou, and F. M. Gasparini, Rev. Sci. Instrum. 61, 1528 (1990).
8. The helium in the connecting lines represents 1.8% by volume of the total sample in the cell. However, due to its small spatial confinement, 0.018 μm × 1 μm, we find that it contributes negligibly to the heat capacity.
9. S. Mehta, M. O. Kimball, and F. M. Gasparini, J. Low Temp. Phys. 114, 467 (1999).
10. M. O. Kimball, S. Mehta, and F. M. Gasparini, J. Low Temp. Phys. 121, 29 (2000).
11. For a review of finite-size scaling, see M. N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1983), Vol. 8; V. Privman, Finite Size Scaling and Numerical Simulations of Statistical Systems (Ref. [3]).
12. For a review of finite-size scaling, see M. N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1983), Vol. 8; V. Privman, Finite Size Scaling and Numerical Simulations of Statistical Systems (Ref. [3]).
13. The exponents α and ν have been obtained in a variety of experiments and theoretical calculations. For the latest experimental determinations, see J. Lipa, D. R. Swanson, J. A. Nissen, T. C. P. Chui, and U. Israelsson, Phys. Rev. Lett. 76, 944 (1996); L.S. Goldner, N. Mulders, and G. Ahlers, J. Low Temp. Phys. 93, 131 (1993); for theory, see M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 61, 5905 (2000).
14. The exponents α and ν have been obtained in a variety of experiments and theoretical calculations. For the latest experimental determinations, see J. Lipa, D. R. Swanson, J. A. Nissen, T. C. P. Chui, and U. Israelsson, Phys. Rev. Lett. 76, 944 (1996); L.S. Goldner, N. Mulders, and G. Ahlers, J. Low Temp. Phys. 93, 131 (1993); for theory, see M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 61, 5905 (2000).
15. The exponents α and ν have been obtained in a variety of experiments and theoretical calculations. For the latest experimental determinations, see J. Lipa, D. R. Swanson, J. A. Nissen, T. C. P. Chui, and U. Israelsson, Phys. Rev. Lett. 76, 944 (1996); L.S. Goldner, N. Mulders, and G. Ahlers, J. Low Temp. Phys. 93, 131 (1993); for theory, see M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 61, 5905 (2000).
16. R. Schmolke, A. Wacker, V. Dohm, and D. Frank, Physica (Amsterdam) 575B, 165 (1990); see also V. Dohm, Phys. Scr. T49, 46 (1993).
17. R. Schmolke, A. Wacker, V. Dohm, and D. Frank, Physica (Amsterdam) 575B, 165 (1990); see also V. Dohm, Phys. Scr. T49, 46 (1993).
18. U. Mohr and V. Dohm, Physica (Amsterdam) 284B-288B, 43 (2000).
19. J. A. Lipa et al., Phys. Rev. Lett. 84, 4894 (2000).
20. J. A. Lipa, M. Coleman, and D. A. Stricker, J. Low Temp. Phys. 124, 443 (2001).
21. N. Schultka and E. Manousakis, J. Low Temp. Phys. 111, 783 (1998).
22. K. Nho and E. Manousakis, Phys. Rev. B 68, 174503 (2003).