Abstract
The “melting” of self-formed rigid structures made of a small number of interacting classical particles confined in an irregular two-dimensional space is investigated using Monte Carlo simulations. It is shown that the interplay of long-range Coulomb repulsions between these particles and the irregular confinement yields a solid-like phase at low temperatures that possesses a bond-orientational order, however, the positional order is depleted even at the lowest temperatures. Upon including thermal fluctuations, this solid-like phase smoothly crosses over to a liquid-like phase by destroying the bond-orientational order. The collapse of solidity is shown to be defect mediated, and aided by the proliferation of free disclinations. The behaviour of different physical observables across the crossover region is studied. These results will help us quantifying the melting found in experiments on systems with confined geometries.
Similar content being viewed by others
References
K. Huang, Statistical Mechanics (Wiley, New York, 1963)
A.R. Ubbelohde, Melting and Crystal Structure (University Press, Oxford, 1965)
T.V. Ramakrishnan, M. Yussouff, Phys. Rev. B 19, 2775 (1979)
D. Frenkel, J.P. McTague, Ann. Rev. Phys. Chem. 31, 491 (1980)
K.J. Strandburg, Rev. Mod. Phys. 60, 161 (1988)
A. Gelfert, W. Nolting, J. Phys.: Condens. Matter 13, 505 (2001)
N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1966)
C.N. Yang, T.D. Lee, Phys. Rev. 87, 404 (1952)
A. Ghosal, A.D. Güclü, C.J. Umrigar, D. Ullmo, H.U. Baranger, Nat. Phys. 2, 336 (2006)
A. Schella, T. Miksch, A. Melzer, J. Schablinski, B. Dietmar, A. Piel, H. Thomsen, P. Ludwig, M. Bonitz, Phys. Rev. E 84, 056402 (2011)
I.M. Buluta, S. Hasegawa, J. Phys. B 42, 154004 (2009)
D.G Rees, I. Kuroda, C.A. Marrache-Kikuchi, M. Höfer, P. Leiderer, K. Kono, J. Low. Temp. Phys. 166, 107 (2012)
C. Yannouleas, U. Landman, Rep. Prog. Phys. 70, 2067 (2007)
A. Melzer, B. Buttenschön, T. Miksch, M. Passvogel, D. Block, O. Arp, A. Piel, Plasma Phys. Control. Fusion 52, 124028 (2010)
E. Wigner, Phys. Rev. 46, 1002 (1934)
B. Tanatar, D.M Ceperley, Phys. Rev. B 39, 5005 (1989)
R. Egger, W. Häusler, C.H. Mak, H. Grabert, Phys. Rev. Lett. 82, 3320 (1999)
A.V. Filinov, M. Bonitz, Yu.E. Lozoviki, Phys. Rev. Lett. 86, 3851 (2001)
A. Ghosal, A.D. Güclü, C.J. Umrigar, D. Ullmo, H.U. Baranger, Phys. Rev. B 76, 085341 (2007)
A.D. Güclü, A. Ghosal, C.J. Umrigar, H.U. Baranger, Phys. Rev. B 77, 041301 (2008)
R.C. Gann, S. Chakravarty, G.V. Chester, Phys. Rev. B 20, 326 (1979)
J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)
B.I. Halperin, D.R. Nelson, Phys. Rev. Lett. 41, 121 (1978)
A.P. Young, Phys. Rev. B 19, 1855 (1979)
D.R. Nelson, B.I. Halperin, Phys. Rev. B 19, 2457 (1979)
V.M. Bedanov, F.M. Peeters, Phys. Rev. B 49, 2667 (1994)
J. Schablinski, D. Block, A. Piel, A. Melzer, H. Thomsen, H. Kählert, M. Bonitz, Phys. Plasmas 19, 013705 (2012)
H.M. Thomas, G.E. Morfill, J. Vac. Sci. Technol. A 14, 501 (1994)
V. Nosenko, J. Goree, A. Piel, Phys. Plasmas 13, 032106 (2006)
P.N. Walker, G. Montambaux, Y. Gefen, Phys. Rev. B 60, 2541 (1999)
C.M. Marcus et al., Chaos Solitons Fractals 8, 1261 (1997)
U. Sivan, R. Berkovits, Y. Aloni, O. Prus, A. Auerbach, G. Ben-Yoseph, Phys. Rev. Lett. 77, 1123 (1996)
Y. Alhassid, Rev. Mod. Phys. 72, 895 (2000)
I.L. Aleiner, P.W. Brouwer, L.I. Glazman, Phys. Rep. 358, 309 (2002)
E. Abrahams, S.V. Kravchenko, M.P. Sarachik, Rev. Mod. Phys. 73, 251 (2001)
S.T. Chui, B. Tanatar, Phys. Rev. Lett. 74, 458 (1995)
X. Waintal, Phys. Rev. B 73, 075417 (2006)
B. Spivak, S.A. Kivelson, Ann. Phys. 321, 2071 (2006)
A.A. Koulakov, F.G. Pikus, B.I. Shklovskii, Phys. Rev. B 55, 9223 (1996)
P.N. Walker, G. Montambaux, Y. Gefen, Phys. Rev. B 60, 2541 (1999)
S.W.S. Apolinario, B. Partoens, F.M. Peeters, Phys. Rev. E 74, 031107 (2006)
B. Reusch, R. Egger, Europhys. Lett. 64, 84 (2003)
O. Bohigas, S. Tomsovic, D. Ullmo, Phys. Rep. 223, 43 (1993)
D. Ullmo, T. Nagano, S. Tomsovic, Phys. Rev. Lett. 90, 176801 (2003)
H. Jiang, H.U. Baranger, W. Yang, Phys. Rev. Lett. 90, 026806 (2003)
A. Ghosal, C.J. Umrigar, H. Jiang, D. Ullmo, H.U. Baranger, Phys. Rev. B 71, 241306 (2005)
V. Cěrný, J. Opt. Theory Appl. 45, 42 (1985)
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)
S. Kirkpatrick, C.D. Gelatt Jr., M.P. Vecchi, Science 220, 4598 (1983)
M.A. Bates, D. Frenkel, Phys. Rev. E 61, 5223 (2000)
E. Tosatti, in The Structure of Surface II, edited by J.F. vander Veen, M.A.V. Howe (Springer, Berlin, 1988), pp. 535-544
J.G. Dash, Contemp. Phys. 30, 89 (1989)
V.J. Goldman, M. Santos, M. Shayegan, J.E. Cunningham Phys. Rev. Lett. 65, 2189 (1990)
B. Spivak, S. Kivelson, J. Phys. IV 131, 255 (2006)
F.A. Lindemann, Z. Phys. 11, 609 (1910)
L. Landau, E. Lifshitz, Statistical Physics (MA: Addison-Wesley, Reading, 1969)
J. Böning, A. Filinov, P. Ludwig, H. Baumgartner, M. Bonitz, Yu.E. Lozovik, Phys. Rev. Lett. 100, 113401 (2008)
A. Filinov, J. Böning, M. Bonitz, Yu.E. Lozovik, Phys. Rev. B 77, 214527 (2008)
V.M. Bedanov, G.V. Gadiyak, Yu.E. Lozovik, Phys. Lett. 109A, 289 (1985)
V.M. Bedanov, G.V. Gadiyak, Yu.E. Lozovik, IEEE Trans. Plasma Sci. 35, 332 (2007)
P. Hartmann, Z. Donkö, P.M. Bakshi, G.J. Kalman, S. Kyrkos, IEEE Trans. Plasma Sci. 35, 332 (2007)
E.L. Cussler, Diffusion: Mass Transfer in Fluid Sphere, 3rd edn. (Cambridge University Press, Cambridge, 2009)
P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Phys. Rev. B 28, 784 (1983)
T. Ott, M. Stanley, M. Bonitz, Phys. Plasmas 18, 063701 (2011)
R.A. Quinn, C. Cui, J. Goree, B. Pieper, H. Thomas, G.E. Morfill, Phys. Rev. E 53, R2049 (1996)
E. Yurtsever, F. Calvo, Molecular Physics 106, 289 (2008)
R. Klein, Computational Geometry and its Applications 333, 148 (1988)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bhattacharya, D., Ghosal, A. Melting of Coulomb-interacting classical particles in 2D irregular traps. Eur. Phys. J. B 86, 499 (2013). https://doi.org/10.1140/epjb/e2013-40568-2
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2013-40568-2