Determination of the critical exponents for the isotropic-nematic phase transition in a system of long rods on two-dimensional lattices: Universality of the transition

Matoz-Fernandez, D. A.; Linares, Daniel; Ramírez-Pastor, A. J.

doi:10.1209/0295-5075/82/50007

Cited by 61 publications

(111 citation statements)

References 24 publications

(28 reference statements)

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“…12). To compare with the first transition from the LDD phase to the nematic phase, ρ * 1 = 0.745 ± 0.010, and the numerical estimate for the exponent ν is consistent with the known exact Ising value 1 [14].…”

Section: A Square Latticementioning

confidence: 54%

“…This transition has also been studied in detail through Monte Carlo simulations [14][15][16][17]. On the square lattice, the transition is numerically found to be in the Ising (equivalently the liquid-gas) universality class [14,18], and on the triangular lattices, it is in the q = 3 Potts model universality class [14,15]. In this paper, we investigate whether the high-density disordered phase is a reentrant low-density disordered phase, or a new qualitatively distinct phase.…”

Section: Introductionmentioning

confidence: 98%

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Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

et al. 2013

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We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length k on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for k = 7. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale ξ * 1400, on the square lattice. For distances smaller than ξ * , correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we cannot rule out a crossover to Ising universality class at length scales ≫ ξ * . On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class.

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Section: A Square Latticementioning

confidence: 54%

Section: Introductionmentioning

confidence: 98%

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

et al. 2013

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“…On the other hand, numerous experimental and numerical studies have been recently devoted to the analysis of equilibrium properties in systems of non-spherical particles [18,19,20,21,22,23,24,25,26]. Of special interest are those studies dealing with lattice versions of the present problem, where the situation is much less clear than in the continuum case.…”

Section: Introductionmentioning

confidence: 99%

Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

2012

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Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length k (k-mers) on twodimensional square lattices. The k-mers, containing k identical units (each one occupying a lattice site), were adsorbed at equilibrium on the lattice. The process was monitored by following the probability R L,k (θ) that a lattice composed of L × L sites percolates at a concentration θ of sites occupied by particles of size k. A nonmonotonic size dependence was observed for the percolation threshold, which decreases for small particles sizes, goes through a minimum, and finally asymptotically converges towards a definite value for large segments. This striking behavior has been interpreted as a consequence of the isotropic-nematic phase transition occurring in the system for large values of k. Finally, the universality class of the model was found to be the same as for the random percolation model.

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“…This value is interesting because it coincides with the minimum value of k (k min = 7), which allows the formation of a nematic phase in long straight rigid rods of length k (k-mers and monodisperse case), on a square or triangular lattice. [11][12][13] The average rod length on the critical line was also obtained for triangular and honeycomb lattices, see Fig. 4.…”

Section: Critical Average Rod Lengthsmentioning

confidence: 82%

“…Finally, Tavares et al 9 assumed as working hypothesis that the nature of the IN transition remains unchanged with respect to the case of monodisperse rigid rods on square lattices, where the transition is in the 2D Ising universality class. [11][12][13][14] From the seminal work by Tavares et al, 9 a series of papers exploring the self-assembled rigid rods (SARRs) model have been published. [15][16][17][18][19][20][21][22][23] These studies can be separated in two groups: (i) those dealing with the nature and universality of the phase transition occurring in the system [15][16][17][18][19][20][21] and (ii) those dealing with the temperature-coverage phase diagram of the system.…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations

López

Linares

Ramírez-Pastor

et al. 2013

The Journal of Chemical Physics

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The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SARRs) model, the surface is represented by a two-dimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular, and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Peierls analytical predictions about the orientational transition for the square and triangular lattices. The analysis of the phase diagrams, along with the behavior of the critical average rod lengths, showed that the critical properties of the model do not depend on the structure of the lattice at low temperatures (coverage), revealing a quasi-one-dimensional behavior in this regime. Finally, the universality class of the SARRs model, which has been subject of controversy, has been revisited.

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Determination of the critical exponents for the isotropic-nematic phase transition in a system of long rods on two-dimensional lattices: Universality of the transition

Cited by 61 publications

References 24 publications

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations

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