We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length $\sigma$, where the particles are confined between two parallel walls and only nearest-neighbor interactions occur. As in our previous work [Gurin, Varga, and Odriozola, Phys. Rev. E 94, 050603 (2016)], the transfer operator method is used, but here we impose a restricted orientation and position approximation to yield an analytic description of the physical properties. This allows us to study the parallel fluid-like to zigzag solid-like structural transition, where the compressibility and heat capacity peaks sharpen and get higher as $H\to H_c=2\sqrt{2}-1\approx 1.8284$ and $p\to p_c=\infty$. Here $H$ is the width of the channel measured in $\sigma$ units and $p$ is the pressure. We have found that this structural change becomes critical at the $(p_c,H_c)$ point. The obtained critical exponents belong to the universality class of the one-dimensional Ising model. We believe this behavior holds for the unrestricted orientational and positional case.

• Received 3 March 2017

DOI:https://doi.org/10.1103/PhysRevE.95.042610