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

Kundu, Joyjit; Rajesh, R.; Dhar, Deepak; Stilck, Jürgen F.

doi:10.1103/physreve.87.032103

Cited by 67 publications

(143 citation statements)

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“…On two-dimensional lattices, remarkably, there are two entropy driven transitions for long rods: first from a low density disordered (LDD) phase to an intermediate density nematic phase, and second from the nematic phase to a high density disordered (HDD) phase [11]. While the existence of the first transition has been proved rigorously [12], the second transition has been demonstrated only numerically [13]. In this paper, we consider a model of rods interacting via a repulsive potential on the random locally tree like layered lattice, and through an exact solution show the existence of two phase transitions as the density is varied.…”

Section: Introductionmentioning

confidence: 99%

Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice

Kundu

Rajesh

2013

Phys. Rev. E

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We solve exactly a model of monodispersed rigid rods of length k with repulsive interactions on the random locally tree like layered lattice. For k ≥ 4 we show that with increasing density, the system undergoes two phase transitions: first from a low density disordered phase to an intermediate density nematic phase and second from the nematic phase to a high density re-entrant disordered phase. When the coordination number is 4, both the phase transitions are continuous and in the mean field Ising universality class. For even coordination number larger than 4, the first transition is discontinuous while the nature of the second transition depends on the rod length k and the interaction parameters.

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Section: Introductionmentioning

confidence: 99%

Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice

Kundu

Rajesh

2013

Phys. Rev. E

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“…We remark that athermal lattice gases with exclusion of neighbors have been considered in literature for several ranges of exclusion (or particle sizes) [19,20] as well as mixtures of them [21]. Furthermore, isotropic-nematic transitions in rigid rods is a problem largely studied (see e. g. [22,24] for recent surveys). However, for the best of our knowledge, rigid rods with neighbor exclusion has been considered only in the case of dimers with NN exclusion [23] only.…”

Section: Thermodynamic Properties Of Modelmentioning

confidence: 99%

Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice

Oliveira

2016

J. Phys. A: Math. Theor.

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The exact grand-canonical solution of a generalized interacting self-avoid walk (ISAW) model, placed on a Husimi lattice built with squares, is presented. In this model, beyond the traditional interaction ω 1 = e ǫ 1 /k B T between (nonconsecutive) monomers on nearest-neighbor (NN) sites, an additional energy ǫ 2 is associated to next-NN (NNN) monomers. Three definitions of NNN sites/interactions are considered, where each monomer can have, effectively, at most 2, 4 or 6 NNN monomers on the Husimi lattice. The phase diagrams found in all cases have (qualitatively) the same thermodynamic properties: a non-polymerized (NP) and a polymerized (P) phase separated by a critical and a coexistence surface that meet at a tricritical (θ-) line. This θ-line is found even when one of the interactions is repulsive, existing for ω 1 in the range [0, ∞), i. e., for ǫ 1 /k B T in the range [−∞, ∞). Counterintuitively, a θ-point exists even for an infinite repulsion between NN monomers (ω 1 = 0), being associated to a coil-"soft globule" transition. In the limit of an infinite repulsive force between NNN monomers, however, the coil-globule transition disappears and only a NP-P continuous transition is observed. This particular case, with ω 2 = 0, is also solved exactly on the square lattice, using a transfer matrix calculation, where a discontinuous NP-P transition is found. For attractive and repulsive forces between NN and NNN monomers, respectively, the model becomes quite similar to the semiflexible-ISAW one, whose crystalline phase is not observed here, as a consequence of the frustration due to competing NN and NNN forces. The mapping of the phase diagrams in canonical ones is discussed and compared with recent results from Monte Carlo simulations.

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“…When k = 2 (dimers), the system is known to be disordered at all densities [25][26][27][28]. When k ≥ 7, there are, interestingly, two transitions: first, from a low-density disordered to an intermediate density nematic phase and second, from the nematic to a highdensity disordered phase [29,30]. While the first transition belongs to the Ising (three state Potts) universality class for the square (triangular) lattice [31], the universality class of the second transition remains unclear with the numerically obtained critical exponents differing from those of the first transition, though a crossover to the Ising exponents at larger length scales could not be ruled out [30,32].…”

mentioning

confidence: 99%

“…When k ≥ 7, there are, interestingly, two transitions: first, from a low-density disordered to an intermediate density nematic phase and second, from the nematic to a highdensity disordered phase [29,30]. While the first transition belongs to the Ising (three state Potts) universality class for the square (triangular) lattice [31], the universality class of the second transition remains unclear with the numerically obtained critical exponents differing from those of the first transition, though a crossover to the Ising exponents at larger length scales could not be ruled out [30,32]. Exact analysis, restricted to a rigorous proof for existence of the first transition when k ≫ 1 [33] and exact solution on a Bethe-like lattice [34] does not shed p-1 any light on the second transition.…”

mentioning

confidence: 99%

“…For fixed fugacities z k1 and z k2 , the system reaches an equilibrium density ρ(z k1 , z k2 ), defined as the fraction of sites occupied by the rods. This algorithm is an adaptation of the scheme that was quite efficient in equilibrating systems of monodispersed long rods [30,49]. Variants of this algorithm have been used to study systems of hard rectangles [50][51][52], disks on square lattice [53] and mixtures of squares and dimers [55].…”

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Phase diagram of a bidispersed hard-rod lattice gas in two dimensions

Kundu¹,

Stilck²,

Rajesh³

2015

EPL

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-We obtain, using extensive Monte Carlo simulations, virial expansion and a highdensity perturbation expansion about the fully packed monodispersed phase, the phase diagram of a system of bidispersed hard rods on a square lattice. We show numerically that when the length of the longer rods is 7, two continuous transitions may exist as the density of the longer rods in increased, keeping the density of shorter rods fixed: first from a low-density isotropic phase to a nematic phase, and second from the nematic to a high-density isotropic phase. The difference between the critical densities of the two transitions decreases to zero at a critical density of the shorter rods such that the fully packed phase is disordered for any composition. When both the rod lengths are larger than 6, we observe the existence of two transitions along the fully packed line as the composition is varied. Low-density virial expansion, truncated at second virial coefficient, reproduces features of the first transition. By developing a high-density perturbation expansion, we show that when one of the rods is long enough, there will be at least two isotropic-nematic transitions along the fully packed line as the composition is varied. and adsorbed gas molecules on metal surfaces [11][12][13][14][15]. A system of hard sphero-cylinders in three-dimensional continuum undergoes a transition from an isotropic phase to an orientationally ordered nematic phase as density is increased. Further increase in density leads to a smectic phase with partial translational order and a solid phase [10,[16][17][18][19][20]. In two-dimensional continuum, a Kosterlitz-Thouless transition to a high-density phase with power law correlations may be observed [21][22][23][24]. Lattice models of hard rods, of interest to this paper, also have a rich phase diagram in two dimensions, while not much is known in three dimensions.

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

Cited by 67 publications

References 31 publications

Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice

Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice

Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice

Phase diagram of a bidispersed hard-rod lattice gas in two dimensions

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