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By mapping the system exactly onto a pair of coupled Ising chains in the thermodynamic limit, we may obtain closed-form expressions for all correlation functions. The coupling between orientational and layer degrees of freedom produces remarkably rich behavior, including crossovers between ferromagnetic and antiferromagnetic orientational order, and states with polarized layers. Despite its simplicity, this exactly soluble model reproduces qualitative features of bent-core smectic liquid crystals and confined colloids, providing insight into the subtle role of particle geometry in driving structural correlations.<\/jats:p>","DOI":"10.1063\/5.0303717","type":"journal-article","created":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T13:27:22Z","timestamp":1770730042000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Bananas for Tonks\u2019 gas: Structural transitions in bent-core molecule bi-layers"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9521-6733","authenticated-orcid":false,"given":"David A.","family":"King","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, University of Pennsylvania , 209 South 33rd St., Philadelphia, Pennsylvania 19104,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2026,2,10]]},"reference":[{"key":"2026021008271570300_c1","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1038\/nmat4178","volume":"14","year":"2015","journal-title":"Nat. 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