Phase diagram of hard squares in slit confinement

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-[Formula: see text] and a zigzag 2-[Formula: see text] structures for H(c)(2) = (2[Formula: see text] − 1) < H < 2, and also another one involving the 1-[Formula: see text] and 2-[Formula: see text] structures (two parallel rows) for 2 < H < H(c)(3) (H(c)(n) = n − 1 + [Formula: see text] /n is the critical wall-to-wall distance for a (n − 1)-[Formula: see text] to n-[Formula: see text] transition and where n-[Formula: see text] represents a structure formed by tilted rectangles, each one clustering n stacked squares), and a triple point for H(t) [Formula: see text] 2.005. In this triple point there coexists the 1-[Formula: see text] , 2-[Formula: see text] , and 2-[Formula: see text] 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)-[Formula: see text] to a n-[Formula: see text] strong transition for H(c)(n) < H < n, followed by a softer (n − 1)-[Formula: see text] to n-[Formula: see text] transition for n < H < H(c)(n + 1). Again, at H [Formula: see text] n there appears a triple point, involving the (n − 1)-[Formula: see text] , n-[Formula: see text] , and n-[Formula: see text] 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 ∈ [Formula: see text] , n > 2), where structures (n − 1)-[Formula: see text] , n-[Formula: see text] , and n-[Formula: see text] fill the phase diagram. Simulation and Onsager theory results are qualitatively consistent.