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For the relevant range of densities, the ground state of the Skyrmemodel on the three torus is shown to correspond to configurations with different symmetries, with a sequence of phase transitions between such configurations. The effects of nonzero finite isospin asymmetry are taken into account by the canonical quantization of isospin collective coordinates, and some thermodynamical and nuclear observables (such as the symmetry energy) are computed as a function of the density. We also explore the extension of the model to accommodate strange degrees of freedom, and find a first-order transition for the condensation of kaons in the Skyrme crystal background in a thermodynamically consistent, non-perturbative way. Finally, an approximate EOS of dense matter is constructed by fitting the free parameters of the model to some nuclear observables close to saturation density, which are particularly relevant for the description of nuclear matter. The resulting neutron star mass\u2013radius curves already reasonably satisfy current astrophysical constraints.<\/jats:p>","DOI":"10.3390\/sym15040899","type":"journal-article","created":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T02:29:15Z","timestamp":1681352955000},"page":"899","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Skyrme Crystals, Nuclear Matter and Compact Stars"],"prefix":"10.3390","volume":"15","author":[{"given":"Christoph","family":"Adam","sequence":"first","affiliation":[{"name":"Department of Particle Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain"},{"name":"Galician Institute of High Energy Physics (IGFAE), E-15782 Santiago de Compostela, Spain"}]},{"given":"Alberto Garc\u00eda","family":"Mart\u00edn-Caro","sequence":"additional","affiliation":[{"name":"Department of Particle Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain"},{"name":"Galician Institute of High Energy Physics (IGFAE), E-15782 Santiago de Compostela, Spain"}]},{"given":"Miguel","family":"Huidobro","sequence":"additional","affiliation":[{"name":"Department of Particle Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain"},{"name":"Galician Institute of High Energy Physics (IGFAE), E-15782 Santiago de Compostela, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0353-4812","authenticated-orcid":false,"given":"Andrzej","family":"Wereszczynski","sequence":"additional","affiliation":[{"name":"Institute of Physics, Jagiellonian University, 31-007 Krakow, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/0003-4916(74)90208-5","article-title":"A Theory of highly condensed matter","volume":"83","author":"Walecka","year":"1974","journal-title":"Ann. 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