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The process of melting water monolayers and quasi-two-dimensional confined water involves, as an intermediate stage, the hexatic phase\u2014a state that lies between solid and liquid and is characterized by quasi-long-range orientational order and short-range translational order. However, the influence of hydrogen bond (HB) cooperativity in this process has not been thoroughly investigated. This gap hampers our understanding of the phase behavior of confined water and limits the accuracy of our models. To address this, we extend the water model developed by Franzese and Stanley, which explicitly includes many-body interactions (MBIs) of HBs. We distinguish the contributions of three-body and five-body HB-MBIs. Our Monte Carlo calculations in the isobaric\u2013isothermal ensemble produce a detailed pressure\u2013temperature phase diagram, revealing polymorphism and polyhexaticity: low-density square ice and high-density triangular ice are separated from the liquid phase by distinct hexatic phases. Three-body interactions notably promote crystallization and can destabilize the low-density hexatic phase, while cooperative five-body interactions help restore it, thus modifying the thermodynamic landscape. These findings demonstrate that HB-MBIs are key to determining the phase behavior of confined water, influencing phenomena such as non-monotonic specific heat, maximum-density lines, and the accessibility of the liquid\u2013liquid critical point. Beyond advancing theoretical understanding, these results have wide-ranging implications for nanofluidics, interfacial science, and applications in biology, food technology, and pharmaceutics, where controlling water under confinement is essential.<\/jats:p>","DOI":"10.1063\/5.0325448","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T15:52:06Z","timestamp":1777909926000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Many-body contributions to polymorphism and polyhexaticity in a water monolayer"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1242-2377","authenticated-orcid":false,"given":"Oriol","family":"Vilanova","sequence":"first","affiliation":[{"name":"F\u00edsica Estad\u00edstica i Interdisciplin\u00e0ria\u2013Departament de F\u00edsica de la Mat\u00e8ria Condensada, Facultat de F\u00edsica, Universitat de Barcelona 1 , Mart\u00ed i Franqu\u00e8s 1, Barcelona 08028,","place":["Spain"]},{"name":"Institut de Nanoci\u00e8ncia i Nanotecnologia de la Universitat de Barcelona (IN2UB) 2 , Diagonal 645, Barcelona 08028,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3006-2766","authenticated-orcid":false,"given":"Giancarlo","family":"Franzese","sequence":"additional","affiliation":[{"name":"F\u00edsica Estad\u00edstica i Interdisciplin\u00e0ria\u2013Departament de F\u00edsica de la Mat\u00e8ria Condensada, Facultat de F\u00edsica, Universitat de Barcelona 1 , Mart\u00ed i Franqu\u00e8s 1, Barcelona 08028,","place":["Spain"]},{"name":"Institut de Nanoci\u00e8ncia i Nanotecnologia de la Universitat de Barcelona (IN2UB) 2 , Diagonal 645, Barcelona 08028,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"2026050411520352900_c1","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1126\/science.1211694","volume":"335","year":"2012","journal-title":"Science"},{"key":"2026050411520352900_c2","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1007\/s11483-010-9198-4","volume":"6","year":"2010","journal-title":"Food Biophys."},{"key":"2026050411520352900_c3","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10867-011-9235-7","volume":"38","year":"2012","journal-title":"J.\u00a0Biol. 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