2000 character limit reached
Inverse renormalization group of spin glasses (2310.12631v2)
Published 19 Oct 2023 in cond-mat.stat-mech, cond-mat.dis-nn, cs.LG, and hep-lat
Abstract: We propose inverse renormalization group transformations to construct approximate configurations for lattice volumes that have not yet been accessed by supercomputers or large-scale simulations in the study of spin glasses. Specifically, starting from lattices of volume $V=8{3}$ in the case of the three-dimensional Edwards-Anderson model we employ machine learning algorithms to construct rescaled lattices up to $V'=128{3}$, which we utilize to extract two critical exponents. We conclude by discussing how to incorporate numerical exactness within inverse renormalization group methods of disordered systems, thus opening up the opportunity to explore a sustainable and energy-efficient generation of exact configurations for increasing lattice volumes without the use of dedicated supercomputers.
- M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications (World Scientific, Singapore, 1987).
- A. Young, Spin Glasses and Random Fields, Directions in condensed matter physics (World Scientific, 1998).
- R. N. Bhatt and A. P. Young, Search for a transition in the three-dimensional j ising spin-glass, Phys. Rev. Lett. 54, 924 (1985).
- F. Haake, M. Lewenstein, and M. Wilkens, Relation of random and competing nonrandom couplings for spin-glasses, Phys. Rev. Lett. 55, 2606 (1985).
- B. W. Southern and A. P. Young, Real space rescaling study of spin glass behaviour in three dimensions, Journal of Physics C: Solid State Physics 10, 2179 (1977).
- J.-S. Wang and R. H. Swendsen, Monte carlo renormalization-group study of ising spin glasses, Phys. Rev. B 37, 7745 (1988a).
- D. Bachtis, Overlap renormalization group transformations for disordered systems 10.48550/arxiv.2302.08459 (2023).
- H. G. Katzgraber, M. Körner, and A. P. Young, Universality in three-dimensional ising spin glasses: A monte carlo study, Phys. Rev. B 73, 224432 (2006).
- D. Ron, R. H. Swendsen, and A. Brandt, Inverse monte carlo renormalization group transformations for critical phenomena, Phys. Rev. Lett. 89, 275701 (2002).
- S. Efthymiou, M. J. S. Beach, and R. G. Melko, Super-resolving the ising model with convolutional neural networks, Phys. Rev. B 99, 075113 (2019).
- S.-H. Li and L. Wang, Neural network renormalization group, Phys. Rev. Lett. 121, 260601 (2018).
- R. H. Swendsen, Phase transitions : Cargese 1980 / edited by Maurice Levy and Jean-Claude Le Guillou and Jean Zinn-Justin (Plenum Press : NATO Scientific Affairs Division New York, 1982).
- D. Bachtis, Reducing finite-size effects in quantum field theories with the renormalization group 10.48550/arxiv.2205.08156 (2022).
- G. Parisi, Infinite number of order parameters for spin-glasses, Phys. Rev. Lett. 43, 1754 (1979).
- G. Parisi, Order parameter for spin-glasses, Phys. Rev. Lett. 50, 1946 (1983).
- S. F. Edwards and P. W. Anderson, Theory of spin glasses, Journal of Physics F: Metal Physics 5, 965 (1975).
- K. Hukushima and K. Nemoto, Exchange monte carlo method and application to spin glass simulations, Journal of the Physical Society of Japan 65, 1604 (1996), https://doi.org/10.1143/JPSJ.65.1604 .
- V. Dumoulin and F. Visin, A guide to convolution arithmetic for deep learning (2018), arXiv:1603.07285 [stat.ML] .
- See Supplemental Material at [URL will be inserted by publisher] for details about the machine learning architecture and the data analysis.
- R. H. Swendsen, Monte carlo renormalization group, Phys. Rev. Lett. 42, 859 (1979).
- J.-S. Wang and R. H. Swendsen, Monte carlo and high-temperature-expansion calculations of a spin-glass effective hamiltonian, Phys. Rev. B 38, 9086 (1988b).
- A. M. Ferrenberg and R. H. Swendsen, New monte carlo technique for studying phase transitions, Phys. Rev. Lett. 61, 2635 (1988).
- F. M. Ytreberg and D. M. Zuckerman, A black-box re-weighting analysis can correct flawed simulation data, Proceedings of the National Academy of Sciences 105, 7982 (2008).