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

Kundu, Joyjit; Rajesh, R.

doi:10.1103/physreve.88.012134

Cited by 23 publications

(35 citation statements)

References 27 publications

(45 reference statements)

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“…When m = 1 and k ≥ 7, there are, remarkably, two entropy-driven transitions: from a low-density isotropic phase to an intermediate density nematic phase, and from the nematic phase to a highdensity disordered phase [18,20]. While the first transition is in the Ising universality class [21,22], the second transition could be non-Ising [20], and it is not yet understood whether the high density phase is a re-entrant low density phase or a new phase [20,23]. When k = 1 (hard squares), the system undergoes a transition into a high * joyjit@imsc.res.in † rrajesh@imsc.res.in density columnar phase.…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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Section: Introductionmentioning

confidence: 99%

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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“…For non-equilibrium 2D systems of rods obtained using a random sequential adsorption (RSA) model, further self-assembly is possible owing to deposition-evaporation processes or to the diffusion motion of particles. Several problems related to such types of self-assembly of rods have previously been discussed [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Sedimentation of a suspension of rods: Monte Carlo simulation of a continuous two-dimensional problem

et al. 2019

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The sedimentation of a two dimensional suspension containing rods was studied by means of Monte Carlo (MC) simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state before sedimentation was produced using a model of random sequential adsorption. During such sedimentation, the rods undergo translational and rotational Brownian motions. The MC simulations were run at different initial number densities (the numbers of rods per unit area), ρi, and sedimentation rates, u. For sediment films, the spatial distributions of the rods, the order parameters and the electrical conductivities were examined. Different types of sedimentation-driven self-assembly and anisotropy of the electrical conductivity were revealed inside the sediment films. This anisotropy can be finely regulated by changes in the values of ρi and u.

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“…The first transition belongs to the Ising universality class on the square lattice [18][19][20] and the three state Potts model universality class on the triangular lattices [19,21]. The nature of the second transition has been difficult to resolve either numerically or analytically [16,17]. On simpler tree-like lattices, the model may also be solved exactly.…”

Section: Introductionmentioning

confidence: 99%

Diffusion dynamics and steady states of systems of hard rods on a square lattice

et al. 2018

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It is known from grand canonical simulations of a system of hard rods on two-dimensional lattices that an orientationally ordered nematic phase exists only when the length of the rods is at least seven. However, a recent microcanonical simulation with diffusion kinetics, conserving both total density and zero nematic order, reported the existence of a nematically phase-segregated steady state with interfaces in the diagonal direction for rods of length six [Phys. Rev. E 95, 052130 (2017)2470-004510.1103/PhysRevE.95.052130], violating the equivalence of different ensembles for systems in equilibrium. We resolve this inconsistency by demonstrating that the kinetics violate detailed balance condition and drives the system to a nonequilibrium steady state. By implementing diffusion kinetics that drive the system to equilibrium, even within this constrained ensemble, we recover earlier results showing phase segregation only for rods of length greater than or equal to seven. Furthermore, in contrast to the nonequilibrium steady state, the interface has no preferred orientational direction. In addition, by implementing different nonequilibrium kinetics, we show that the interface between the phase segregated states can lie in different directions depending on the choice of kinetics.

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

Cited by 23 publications

References 27 publications

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

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

Sedimentation of a suspension of rods: Monte Carlo simulation of a continuous two-dimensional problem

Diffusion dynamics and steady states of systems of hard rods on a square lattice

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