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• W2144551292 abstract "A system of hard rectangles of size $mifmmodetimeselsetexttimesfi{}mk$ on a square lattice undergoes three entropy-driven phase transitions with increasing density for large-enough aspect ratio $k$: first from a low-density isotropic to an intermediate-density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high-density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with $m=1,2$, and 3, that the transition density for the isotropic-nematic transition is $ensuremath{approx}{A}_{1}/k$ when $kensuremath{gg}1$, where ${A}_{1}$ is independent of $m$. We estimate ${A}_{1}=4.80ifmmodepmelsetextpmfi{}0.05$. Within a Bethe approximation and virial expansion truncated at the second virial coefficient, we obtain ${A}_{1}=2$. The critical density for the nematic-columnar transition when $m=2$ is numerically shown to tend to a value less than the full packing density as ${k}^{ensuremath{-}1}$ when $kensuremath{rightarrow}ensuremath{infty}$. We find that the critical Binder cumulant for this transition is nonuniversal and decreases as ${k}^{ensuremath{-}1}$ for $kensuremath{gg}1$. However, the transition is shown to be in the Ising universality class." @default.
• W2144551292 created "2016-06-24" @default.
• W2144551292 creator A5017392702 @default.
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• W2144551292 date "2015-01-06" @default.
• W2144551292 modified "2023-10-18" @default.
• W2144551292 title "Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries for the system of hard rectangles on a square lattice" @default.
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• W2144551292 doi "https://doi.org/10.1103/physreve.91.012105" @default.
• W2144551292 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/25679568" @default.
• W2144551292 hasPublicationYear "2015" @default.
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