Modified Percolation Theory and Its Relevance to Quantum Critical Phenomena


We present a new family of percolation models. We show, using theory and computer simulations, that these represent a new universality class. Interestingly, systems in this class appear to violate the Harris criterion, making model systems within these class ideal systems for studying the influence of disorder on critical behavior. We argue that such percolative systems have already been realized in practice in strongly correlated electron systems that have been driven to the quantum critical point by means of chemical substitution.

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Heitmann, T. , Gaddy, J. and Montfrooij, W. (2014) Modified Percolation Theory and Its Relevance to Quantum Critical Phenomena. Journal of Modern Physics, 5, 649-660. doi: 10.4236/jmp.2014.58076.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Stauffer, D. and Aharony, A. (1994) Introduction to Percolation Theory. CRC, Boca Raton.
[2] Sahimi, M. (1994) Applications of Percolation Theory. Taylor and Francis, London.
[3] Nakayama, T., Yakubo, K. and Orbach, R.L. (1994) Reviews of Modern Physics, 66, 381-443.
[4] Harris, A. (1974) Journal of Physics C: Solid State Physics, 7, 1671-1692.
[5] Stewart, G.R. (2001) Reviews of Modern Physics, 73, 797-855.
[6] Chayes, J., Chayes, L., Fisher, D. and Spencer, T. (1986) Physical Review Letters, 57, 2999-3002.
[7] Levinshtein, M.E., Shklovskii, B.I., Shur, M.S. and Efros, A.L. (1976) Soviet Physics JETP, 42, 197-201.
[8] Sachdev, S. (1999) Quantum Phase Transitions. Cambridge University Press, Cambridge.
[9] Castro-Neto, A.H. and Jones, B.A. (2000) Physal Review B, 62, 14975-15011.
[10] Kondo, J. (1964) Progress in Theoretical Physics, 32, 37-49.
[11] Fontes, F.B., Continentino, M.A., Bud’ko, S.L., El-Massalami, M., Sampaio, L.C., Guimaraes, A.P., Baggio-Saitovitch, E., Hundley, M.F. and Lacerda, A. (1996) Physical Review B, 53, 11678-11684.
[12] Bernal, O.O., MacLaughlin, D.E., Lukefahr, H.G. and Andraka, B. (1995) Physical Review Letters, 75, 2023-2026.
[13] Montfrooij, W., Lamsal, J., Aronson, M., Bennett, M., de Visser, A., Kai, H.Y., Huy, N.T., Yethiraj, M., Lumsden, M. and Qiu, Y. (2007) Physical Review B, 76, 052404-052408.
[14] Montfrooij, W., Aronson, M., Rainford, B.D., Mydosh, J.A., Murani, A.P., Haen, P. and Fukuhara, T. (2003) Physical Review Letters, 91, Article ID: 087202.
[15] Westerkamp, T., Deppe, M., Küchler, R., Brando, M., Geibel, C., Gegenwart, P., Pikul, A.P. and Steglich, F. (2009) Physical Review Letters, 102, 206404-206408.
[16] Garcia Soldervilla, J., Gomez Sal, J.C., Blanco, J.A., Espeso, J.I. and Rodrguez Fernandez, J. (2000) Physical Review B, 61, 6821-6825.
[17] Lausberg, S., Spehling, J., Steppke, A., Jesche, A., Leutkens, H., Amato, A., Baines, C., Krellner, C., Brando, M., Geibel, C., Klauss, H.-H. and Steglich, F. (2012) Physical Review Letters, 109, 216402-216406.
[18] Heitmann, T., Gaddy, J., Lamsal, J. and Montfrooij, W. (2012) Journal of Physics: Conference Series, 391, 012018-012020.
[19] Gaddy, J., Heitmann, T. and Montfrooij, W. (2014) Journal of Applied Physics, 115, 17E110.

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