Abstract
Suppose we have a simple bar magnet. We know it is a ferromagnet because it is capable of picking up thumbtacks, the number of which is called the order parameter M. As we heat this system, M decreases and eventually, at a certain critical temperature T c , it reaches zero: no more thumbtacks remain! In fact, the transition is remarkably sharp, since M approaches zero at T c with infinite slope. Such singular behavior is an example of a “critical phenomenon.”
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References
Als-Nielsen, J., and R. J. Birgeneau, 1977, Am. J. Phys. 45, 554.
Brézin, E., and S. R. Wadia, 1993, The Large N Expansion in Quantum Field Theory and Statistical Physics: From Spin Systems to 2-dimensional Gravity (World Scientific, Singapore).
Bunde, A., and S. Havlin, Eds., 1996, Fractals and Disordered Systems, Second Edition (Springer-Verlag, Berlin).
Cardy, J. L., 1996, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, England).
de Gennes, P.-G., 1979, Scaling Concepts in Polymer Physics (Cornell University, Ithaca).
Domb, C., 1996, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena (Taylor & Francis, London).
Fisher, M. E., 1967, Rep. Prog. Phys. 30, 615.
Fisher, M. E., 1974, Rev. Mod. Phys. 46, 597.
Fisher, M. E., 1998, Rev. Mod. Phys. 70, 653.
Goldenfeld, N., 1994, Renormalization Group in Critical Phenomena (Addison-Wesley, Reading).
Hohenberg, P. C., and B. I. Halperin, 1977, Rev. Mod. Phys. 49, 435.
Jackiw, R., 1972, Phys. Today 25, 23.
Kadanoff, L. P., et al., 1967, Rev. Mod. Phys. 39, 395.
Lee, T. D., and C. N. Yang, 1952, Phys. Rev. 87, 410.
Lesne, A., 1998, Renormalization Methods: Critical Phenomena, Chaos, Fractal Structure (Wiley, New York).
Levelt Sengers, J. M. H., R. Hocken, and J. V. Sengers, 1977, Phys. Today 30, 42.
Mantegna, R. N., and H. E. Stanley, 1999 Econophysics: An Introduction (Cambridge University Press, Cambridge, England).
Milošević, S., and H. E. Stanley, 1976, in Local Properties at Phase Transitions, Proceedings of Course 59, Enrico Fermi School of Physics, edited by K. A. Mü ller and A. Rigamonti (North-Holland, Amsterdam), pp. 773–784.
Mishima, O., and H. E. Stanley, 1998, Nature (London) 396, 329.
Nelson, D. R., and M. E. Fisher, 1975, Ann. Phys. (N.Y.) 91, 226.
Peebles, P. J. E., 1980, The Large-Scale Structure of the Universe (Princeton University Press, Princeton, NJ).
Potts, R. B., 1952, Proc. Cambridge Philos. Soc. 48, 106.
Stanley, H. R, 1968, Phys. Rev. Lett. 20, 589.
Stanley, H. E., 1971, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, London).
Stanley, H. E., P. Reynolds, S. Redner, and F. Family, 1982, in Real-Space Renormalization, edited by T. W. Burkhardt and J. M. J. van Leeuwen (Springer-Verlag, Berlin).
Stanley, H. E., L. Cruz, S. T. Harrington, P. H. Poole, S. Sastry, F. Sciortino, F. W. Starr, and R. Zhang, 1997, Physica A 236, 19.
Stauffer, D., and A. Aharony, 1992, Introduction to Percolation Theory (Taylor & Francis, Philadelphia).
Wu, F. Y., 1982, Rev. Mod. Phys. 54, 235.
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Stanley, H.E. (1999). Scaling, Universality, and Renormalization: Three Pillars of Modern Critical Phenomena. In: Bederson, B. (eds) More Things in Heaven and Earth. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1512-7_39
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