### Abstract

This work shows a complete phase diagram of hard squares of side length σ in slit confinement for H < 4.5, H being the wall to wall distance measured in σ units, including the maximal packing fraction limit. The phase diagram exhibits a transition between a single-row parallel 1- □ and a zigzag 2- ⋄ structures for H _{c} (2) = (2-2-1) < H < 2, and also another one involving the 1- □ and 2- □ structures (two parallel rows) for 2 < H < H _{c} (3) (H _{c} (n) = n - 1 +-2n-1/n is the critical wall-to-wall distance for a (n - 1)- □ to n- □ transition and where n- □ represents a structure formed by tilted rectangles, each one clustering n stacked squares), and a triple point for H _{t} ⋄ 2.005. In this triple point there coexists the 1- □, 2- □, and 2- ⋄ structures. For regions H _{c} (3) < H < H _{c} (4) and H _{c} (4) < H < H _{c} (5), very similar pictures arise. There is a (n - 1)- □ to a n- □ strong transition for H _{c} (n) < H < n, followed by a softer (n - 1)- □ to n- □ transition for n < H < H _{c} (n + 1). Again, at H ≳ n there appears a triple point, involving the (n - 1)- □, n- □, and n- □ structures. The similarities found for n = 2, 3 and 4 lead us to propose a tentative phase diagram for H _{c} (n) < H < H _{c} (n + 1) (n ∈ℕ, n > 2), where structures (n - 1)- □, n- □, and n- □ fill the phase diagram. Simulation and Onsager theory results are qualitatively consistent.

Original language | English |
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Article number | 8886 |

Journal | Scientific reports |

Volume | 8 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 2018 |

### ASJC Scopus subject areas

- General

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## Cite this

*Scientific reports*,

*8*(1), [8886]. https://doi.org/10.1038/s41598-018-26922-3