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Communication: The criticality of self-assembled rigid rods on triangular lattices
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Figures

Image of FIG. 1.

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FIG. 1.

Examples of ordered (left) and disordered (right) configurations for the SARR model on triangular lattices. Monomers are represented with thick segments lying on the lattice sites. Two nearest-neighbor monomers interact (and form a bond) if the corresponding segments are in a head-to-tail configuration.

Image of FIG. 2.

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FIG. 2.

Results for the order parameter δ as a function of the reduced temperature for different system sizes (as indicated in the legends); left panel μ/ε = −0.90, right panel μ/ε = −0.95.

Image of FIG. 3.

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FIG. 3.

Fourth-order Binder cumulant at constant μ as a function of T, for different system sizes; left panel μ/ε = −0.90, right panel μ/ε = −0.95. Horizontal lines depict the estimate of g 4c for the two dimensional Potts q = 3 universality class. Vertical lines delimit the unbiased estimates of the critical temperature (see the text for the details).

Image of FIG. 4.

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FIG. 4.

Density and derivative of the density with respect to the temperature at constant chemical potential μ/ε = −0.95.

Tables

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Table I.

Finite-size scaling results from simulation: n is the number of system sizes used to compute critical properties and effective critical exponents. L min and L max are the minimum and maximum system sizes used in the finite-size scaling analysis. The results shown for α/ν were computed from the scaling of (∂ρ/∂T)μ, except for the full lattice case (ρ = 1) where (∂(H/M)/∂T) was used. For finite μ similar values of α/ν were obtained using (∂ρ/∂μ) T or (∂(H/M)/∂T)μ. The critical exponent ratios for Potts q = 1 universality class are β/ν = 5/48 ≃ 0.104, γ/ν = 43/24 ≃ 1.792, 1/ν = 3/4, and α/ν = −1/2. The corresponding values for Potts q = 3 universality class are β/ν = 2/15 ≃ 0.133, γ/ν = 26/15 ≃ 1.733, 1/ν = 6/5, and α/ν = 2/5 (Ref. 15). Error bars are given in parentheses (curly brackets) in units of the last digit of the corresponding quantity.

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/content/aip/journal/jcp/134/7/10.1063/1.3556665
2011-02-15
2014-04-23

Abstract

The criticality of self-assembled rigid rods on triangular lattices is investigated using Monte Carlo simulation. We find a continuous transition between an ordered phase, where the rods are oriented along one of the three (equivalent) lattice directions, and a disordered one. We conclude that equilibrium polydispersity of the rod lengths does not affect the critical behavior, as we found that the criticality is the same as that of monodisperse rods on the same lattice, in contrast with the results of recently published work on similar models.

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Scitation: Communication: The criticality of self-assembled rigid rods on triangular lattices
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/7/10.1063/1.3556665
10.1063/1.3556665
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