Elementary particles in two dimensional systems are not constrained by the fermion-boson alternative. They are so-called "anyons''. Anyon systems are modelled by modular tensor categories, and form an active area of research. Oxford Mathematician André Henriques explains his interest in the question.

Reversible signal transmission in an active mechanical metamaterial.
Browning, A Woodhouse, F Simpson, M Proceedings. Mathematical, physical, and engineering sciences volume 475 issue 2227 20190146 (24 Jul 2019)
Search for PeV Gamma-Ray Emission from the Southern Hemisphere with 5
Years of Data from the IceCube Observatory
Bagherpour, H Argüelles, C Auffenberg, J Anderson, T Ansseau, I Backes, P Anton, G Axani, S Bai, X Bernardini, E Besson, D Blaufuss, E Bindig, D BenZvi, S Berley, D Tjus, J Binder, G Blot, S Brostean-Kaiser, J Busse, R Chirkin, D Burgman, A Buscher, J Carver, T Cheung, E The Astrophysical Journal: an international review of astronomy and astronomical physics (27 Feb 2020)
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