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Complex Systems and Renormalization Group Explanations

Published online by Cambridge University Press:  01 January 2022

Margaret Morrison
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Abstract

Despite the close connection between the central limit theorem and renormalization group (RG) methods, the latter should be considered fundamentally distinct from the kind of probabilistic framework associated with statistical mechanics, especially the notion of averaging. The mathematics of RG is grounded in dynamical systems theory rather than probability, which raises important issues with respect to the way RG generates explanations of physical phenomena. I explore these differences and show why RG methods should be considered not just calculational tools but the basis for a physical understanding of complex systems in terms of structural properties and relations.

Type
Complex Systems
Information
Philosophy of Science , Volume 81 , Issue 5 , December 2014 , pp. 1144 - 1156
Copyright
Copyright © The Philosophy of Science Association

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References

Batterman, Robert. 2010. “Reduction and Renormalization.” In Time, Chance, and Reduction: Philosophical Aspects of Statistical Mechanics, ed. Hüttemann, A. and Ernst, G., 159–79. Cambridge: Cambridge University Press.Google Scholar
Cassandro, M., and Jona-Lasinio, Giovanni. 1978. “Critical Point Behaviour and Probability Theory.” Advances in Physics 27:913–41.10.1080/00018737800101504CrossRefGoogle Scholar
Feigenbaum, Mitchell. 1978. “Quantitative Universality for a Class of Nonlinear Transformations.” Journal of Statistical Physics 19:25–52.10.1007/BF01020332CrossRefGoogle Scholar
Gell-Mann, Murray, and Low, Francis E.. 1954. “Quantum Electrodynamics at Small Distances.” Physical Review 95:1300–1312.10.1103/PhysRev.95.1300CrossRefGoogle Scholar
Gnedenko, B. V., and Kolmogorov, A. N.. 1954. Limit Distributions for Sum of Independent Random Variables. Reading, MA: Addison-Wesley.Google Scholar
Goldenfeld, Nigel, and Kadanoff, Leo. 1999. “Simple Lessons from Complexity.” Science 284:87–89.10.1126/science.284.5411.87CrossRefGoogle ScholarPubMed
Humphreys, Paul. 2014. “Explanation as Condition Satisfaction.” Philosophy of Science, in this issue.10.1086/677698CrossRefGoogle Scholar
Jona-Lasinio, Giovanni. 2001. “Renormalization Group and Probability Theory.” Physics Reports 352:439–58.10.1016/S0370-1573(01)00042-4CrossRefGoogle Scholar
Kadanoff, Leo. 1966. “Scaling Laws for Ising Models near Tc.” Physics 2:263.10.1103/PhysicsPhysiqueFizika.2.263CrossRefGoogle Scholar
Khinchin, Aleksander I. 1949. Mathematical Foundations of Statistical Mechanics. New York: Dover.Google Scholar
Landau, Lev D. 1937. “On the Theory of Phase Transitions.” Trans. and repr. in L. D. Landau, Collected Papers (Moscow: Nauka, 1969), 1:234–52.Google Scholar
Lesne, Annick. 1998. Renormalization Methods: Critical Phenomena, Chaos, Fractal Structures. New York: Wiley.Google Scholar
May, Robert M. 1976. “Simple Mathematical Models with Very Complicated Dynamics.” Nature 261 (5560): 459–67.10.1038/261459a0CrossRefGoogle ScholarPubMed
Onsanger, Lars 1944. “Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition.” Physical Review 65:117–49.Google Scholar
Sornette, Didier. 2000. Critical Phenomena in the Natural Science. Heidelberg: Springer.10.1007/978-3-662-04174-1CrossRefGoogle Scholar
Weinberg, Steven. 1981. “Why the Renormalization Group Is a Good Thing.” In Proceedings: Asymptotic Realms of Physics, 1–19. Cambridge: Cambridge University Press.Google Scholar
Wilson, Kenneth G. 1971a. “Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture.” Physical Review B 4:3174.10.1103/PhysRevB.4.3174CrossRefGoogle Scholar
Wilson, Kenneth G. 1971b. “Renormalization Group and Critical Phenomena. II. Phase Space Cell Analysis of Critical Behaviour.” Physical Review B 4:3184.10.1103/PhysRevB.4.3184CrossRefGoogle Scholar