### Abstract

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 language | English |
---|---|

Article number | 042610 |

Journal | Physical Review E |

Volume | 95 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 27 2017 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E*,

*95*(4), [042610]. https://doi.org/10.1103/PhysRevE.95.042610

**Critical behavior of hard squares in strong confinement.** / Gurin, Péter; Odriozola, Gerardo; Varga, S.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 95, no. 4, 042610. https://doi.org/10.1103/PhysRevE.95.042610

}

TY - JOUR

T1 - Critical behavior of hard squares in strong confinement

AU - Gurin, Péter

AU - Odriozola, Gerardo

AU - Varga, S.

PY - 2017/4/27

Y1 - 2017/4/27

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevE.95.042610

DO - 10.1103/PhysRevE.95.042610

M3 - Article

VL - 95

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

M1 - 042610

ER -