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.