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  1. Idealizations and Analogies: Explaining Critical Phenomena.Quentin Rodriguez - 2021 - Studies in History and Philosophy of Science Part A 89 (C):235-247.
    The “universality” of critical phenomena is much discussed in philosophy of scientific explanation, idealizations and philosophy of physics. Lange and Reutlinger recently opposed Batterman concerning the role of some deliberate distortions in unifying a large class of phenomena, regardless of microscopic constitution. They argue for an essential explanatory role for “commonalities” rather than that of idealizations. Building on Batterman's insight, this article aims to show that assessing the differences between the universality of critical phenomena and two paradigmatic cases of “commonality (...)
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  • History of the Lenz–Ising Model 1950–1965: from irrelevance to relevance.Martin Niss - 2008 - Archive for History of Exact Sciences 63 (3):243-287.
    This is the second in a series of three papers that charts the history of the Lenz–Ising model (commonly called just the Ising model in the physics literature) in considerable detail, from its invention in the early 1920s to its recognition as an important tool in the study of phase transitions by the late 1960s. By focusing on the development in physicists’ perception of the model’s ability to yield physical insight—in contrast to the more technical perspective in previous historical accounts, (...)
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  • History of the Lenz–Ising model 1965–1971: the role of a simple model in understanding critical phenomena.Martin Niss - 2011 - Archive for History of Exact Sciences 65 (6):625-658.
    This is the last in a series of three papers on the history of the Lenz–Ising model from 1920 to the early 1970s. In the first paper, I studied the invention of the model in the 1920s, while in the second paper, I documented a quite sudden change in the perception of the model in the early 1960s when it was realized that the Lenz–Ising model is actually relevant for the understanding of phase transitions. In this article, which is self-contained, (...)
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  • A Mathematician Doing Physics: Mark Kac’s Work on the Modeling of Phase Transitions.Martin Niss - 2018 - Perspectives on Science 26 (2):185-212.
    After World War II, quite a few mathematicians, including Mark Kac, John von Neumann, and Nobert Wiener, worked on the physical problem of phase transitions, i.e. changes in the state of matter caused by gradual changes of physical parameters such as the condensation of a gas to a liquid and the loss of magnetization of a ferromagnet above a certain temperature. The significance of these mathematicians was not so much that they brought mathematical rigor to the theoretical description of the (...)
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  • Becoming Large, Becoming Infinite: The Anatomy of Thermal Physics and Phase Transitions in Finite Systems.David A. Lavis, Reimer Kühn & Roman Frigg - 2021 - Foundations of Physics 51 (5):1-69.
    This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of (...)
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  • On the Renormalization Group Explanation of Universality.Alexander Franklin - 2018 - Philosophy of Science 85 (2):225-248.
    It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...)
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  • Magnets, spins, and neurons: The dissemination of model templates across disciplines.Tarja Knuuttila & Andrea Loettgers - 2014 - The Monist 97 (3):280-300.
    One of the most conspicuous features of contemporary modeling practices is the dissemination of mathematical and computational methods across disciplinary boundaries. We study this process through two applications of the Ising model: the Sherrington-Kirkpatrick model of spin glasses and the Hopfield model of associative memory. The Hopfield model successfully transferred some basic ideas and mathematical methods originally developed within the study of magnetic systems to the field of neuroscience. As an analytical resource we use Paul Humphreys's discussion of computational and (...)
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