Critical behavior of hard squares in strong confinement

Péter Gurin, Gerardo Odriozola, Szabolcs Varga

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4 Citations (Scopus)


We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length σ, 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)]2470-004510.1103/PhysRevE.94.050603, 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→Hc=22-1≈1.8284 and p→pc. Here H is the width of the channel measured in σ units and p is the pressure. We have found that this structural change becomes critical at the (pc,Hc) 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.

Original languageEnglish
Article number042610
JournalPhysical Review E
Issue number4
Publication statusPublished - Apr 27 2017


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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