You have already added 0 works in your ORCID record related to the merged Research product.
You have already added 0 works in your ORCID record related to the merged Research product.
Statistical Physics through the Lens of Real-Space Mutual Information.
Copyright policy )Statistical Physics through the Lens of Real-Space Mutual Information.
Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building.
Comment: Version accepted for publication in Physical Review Letters. See also the companion manuscript arXiv:2103.16887 "Symmetries and phase diagrams with real-space mutual estimation neural estimation"
- University of Zurich Switzerland
- University of Chicago United States
- Physics department University of Zurich Switzerland
- Hebrew University of Jerusalem Israel
- Institute for Quantum Electronics/Physics ETH Zurich Switzerland
Statistical Mechanics (cond-mat.stat-mech), Disordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, Renormalization group; Critical phenomena; Statistical physics; Machine learning; Information theory; Coarse graining, General Physics and Astronomy, Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks
Statistical Mechanics (cond-mat.stat-mech), Disordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, Renormalization group; Critical phenomena; Statistical physics; Machine learning; Information theory; Coarse graining, General Physics and Astronomy, Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks
5916
1 Kadano , L. P. Scaling laws for Ising models near Tc. Phys. Phys. Fiz. 2, 263{272 (1966).
2 Wilson, K. G. & Kogut, J. The renormalization group and the expansion. Phys. Rep. 12, 75 { 199 (1974).
3 Wilson, K. G. The renormalization group: Critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773{840 (1975).
4 Fisher, M. E. Renormalization group theory: Its basis and formulation in statistical physics. Rev. Mod. Phys. 70, 653{681 (1998).
5 Koch-Janusz, M. & Ringel, Z. Mutual information, neural networks and the renormalization group. Nat. Phys. 14, 578{582 (2018).
6 Lenggenhager, P. M., Gokmen, D. E., Ringel, Z., Huber, S. D. & Koch-Janusz, M. Optimal renormalization group transformation from information theory. Phys. Rev. X 10, 011037 (2020).
7 Coveney, P. V., Dougherty, E. R. & High eld, R. R. Big data need big theory too. Philos. Trans. R. Soc. A 374 (2016).
8 Gordon, A., Banerjee, A., Koch-Janusz, M. & Ringel, Z. Relevance in the Renormalization Group and in Information Theory (2020). arXiv:2012.01447.
9 Alet, F. et al. Interacting classical dimers on the square lattice. Phys. Rev. Lett. 94, 235702 (2005).
10 Alet, F., Ikhlef, Y., Jacobsen, J. L., Misguich, G. & Pasquier, V. Classical dimers with aligning interactions on the square lattice. Phys. Rev. E 74, 041124 (2006). [OpenAIRE]
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!
- University of Zurich Switzerland
- University of Chicago United States
- Physics department University of Zurich Switzerland
- Hebrew University of Jerusalem Israel
- Institute for Quantum Electronics/Physics ETH Zurich Switzerland
- ETH Zurich Switzerland
Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building.
Comment: Version accepted for publication in Physical Review Letters. See also the companion manuscript arXiv:2103.16887 "Symmetries and phase diagrams with real-space mutual estimation neural estimation"