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While the role of local interactions in nonequilibrium phase transitions is well studied, a fundamental understanding of the effects of long-range interactions is lacking.
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See Supplemental Material for detailed calculations and technical background information, which includes Refs. Gardiner 2009 ; Doi 1976 ; Peliti, L. 1985 ; Chavanis 2008 ; Dean 1996 ; Kawasaki 1994 ; Caballero et al. 2018b ; Cavagna et al. 2023 ; Kardar 2007 ; Jäger and Luckhaus 1992 ; Bausch et al. 1976 ; Janssen 1976 ; de Dominicis 1976 ; Martin et al. 1973 ; Täuber 2014 ; Tindall et al. 2008 ; Canet et al. 2010 ; Dupuis et al. 2021 ; Mesibov et al. 1973 ; Zinn-Justin 2002 ; Janssen 2005 ; Langtangen and Logg 2017 ; Logg and Wells 2010
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A. Cavagna, L. Di Carlo, I. Giardina, T.S. Grigera, S. Melillo, L. Parisi, G. Pisegna, and M. Scandolo, “Natural swarms in 3.99 dimensions,” Nature Physics (2023), 10.1038/s41567-023-02028-0
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