Hard rigid rods on a Bethe-like lattice

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

doi:10.1103/physreve.84.011140

Cited by 41 publications

(59 citation statements)

References 42 publications

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“…For large enough k, the existence of the nematic phase may be rigorously proved [26]. The model may also be solved exactly on a tree-like lattice, corresponding to a Bethe approxima-tion, and shows a nematic phase for k ≥ 4, but does not exhibit a second transition [27]. Density functional theory for rods give a similar result [28].…”

Section: Introductionmentioning

confidence: 99%

Different phases of a system of hard rods on three dimensional cubic lattice

2017

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We study the different phases of a system of monodispersed hard rods of length k on a cubic lattice using an efficient cluster algorithm which can simulate densities close to the fully-packed limit. For k ≤ 4, the system is disordered at all densities. For k = 5, 6, we find a single density-driven transition from a disordered phase to high density layered-disordered phase in which the density of rods of one orientation is strongly suppressed, breaking the system into weakly coupled layers. Within a layer, the system is disordered. For k ≥ 7, three density driven transitions are observed numerically: isotropic to nematic to layered-nematic to layered-disordered. In the layered-nematic phase, the system breaks up into layers, with nematic order in each in each layer, but very weak correlation between the ordering direction between different layers. We argue that the layered-nematic phase is a finite-size effect, and in the thermodynamic limit, the nematic phase will have higher entropy per site.

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Section: Introductionmentioning

confidence: 99%

Different phases of a system of hard rods on three dimensional cubic lattice

2017

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“…For oriented lines in the continuum (k → ∞), a nematic phase exists at high density [22]. The only theoretical results that exist are when m = 1 and k = 2 (dimers), for which no nematic phase exists [30][31][32][33], k ≫ 1, when the existence of the nematic phase may be proved rigorously [19], and an exact solution for arbitrary k on a tree like lattice [5,23]. Less is known for other values of m and k. Simulations of rectangles of size 2 × 5 did not detect any phase transition with increasing density [34], while those of parallelepipeds on cubic lattice show layered and columnar phases, but no nematic phase [35].…”

Section: Introductionmentioning

confidence: 99%

Phase transitions in a system of hard rectangles on the square lattice

Kundu

Rajesh

2014

Phys. Rev. E

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The phase diagram of a system of monodispersed hard rectangles of size m×mk on a square lattice is numerically determined for m = 2, 3 and aspect ratio k = 1, 2, . . . , 7. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solid-like phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large k are determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger m and k, showing that for k ≥ 7, the system undergoes three entropy driven phase transitions with increasing density. The nature of the different phase transitions are established and the critical exponents for the continuous transitions are determined using finite size scaling.

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“…Recently, we showed that a Bethe-like approximation becomes exact on a random locally tree like layered lattice, and for the 4-coordinated lattice, k min = 4. But on this lattice, the second transition is absent [20].…”

Section: Introductionmentioning

confidence: 99%

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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Hard rigid rods on a Bethe-like lattice

Cited by 41 publications

References 42 publications

Different phases of a system of hard rods on three dimensional cubic lattice

Different phases of a system of hard rods on three dimensional cubic lattice

Phase transitions in a system of hard rectangles on the square lattice

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

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