Stability of columnar order in assemblies of hard rectangles or squares

Nath, Trisha; Dhar, Deepak; Rajesh, R.

doi:10.1209/0295-5075/114/10003

Cited by 22 publications

(33 citation statements)

References 67 publications

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“…For the latter case, it was erroneously assumed in Ref. [6] that the contributions from left and right interfaces are identical.…”

Section: Discussionmentioning

confidence: 99%

“…In our calculations we assumed that the ordered phases have perfect order, thereby ignoring the presence of defects in the bulk phases. Defects may be included in a systematic manner, as was done for the case of 2 × d rectangles [6]. However, it was found that the corrections appearing from including overhangs were more dominant than that arising from including defects when d was small as is the case for hard squares.…”

Section: Discussionmentioning

confidence: 99%

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Columnar-disorder phase boundary in a mixture of hard squares and dimers

Mandal

Rajesh

2017

Phys. Rev. E

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A mixture of hard squares, dimers, and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to a high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes a Kosterliz-Thouless-type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simulations.

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“…For the latter case, it was erroneously assumed in Ref. [6] that the contributions from left and right interfaces are identical.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Columnar-disorder phase boundary in a mixture of hard squares and dimers

Mandal

Rajesh

2017

Phys. Rev. E

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“…We note that in this phase, two sublattices are preferentially occupied, one with A- type particles and the other with B-type particles. The stabilization of the columnar phase by creating vacancies is an example of order by disorder, prototypical example being the hard square gas [13][14][15][16][17][18].…”

Section: Two Types Of Particles (Zmentioning

confidence: 99%

Phase transitions in a system of hard Y-shaped particles on the triangular lattice

2018

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We study the different phases and the phase transitions in a system of Y-shaped particles, examples of which include immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume interactions. Each particle consists of a central site and three of its six nearest neighbors chosen alternately, such that there are two types of particles which are mirror images of each other. We study the equilibrium properties of the system using grand canonical Monte Carlo simulations that implement an algorithm with cluster moves that is able to equilibrate the system at densities close to full packing. We show that, with increasing density, the system undergoes two entropy-driven phase transitions with two broken-symmetry phases. At low densities, the system is in a disordered phase. As intermediate phases, there is a solidlike sublattice phase in which one type of particle is preferred over the other and the particles preferentially occupy one of four sublattices, thus breaking both particle symmetry as well as translational invariance. At even higher densities, the phase is a columnar phase, where the particle symmetry is restored, and the particles preferentially occupy even or odd rows along one of the three directions. This phase has translational order in only one direction, and breaks rotational invariance. From finite-size scaling, we demonstrate that both the transitions are first order in nature. We also show that the simpler system with only one type of particle undergoes a single discontinuous phase transition from a disordered phase to a solidlike sublattice phase with an increasing density of particles.

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“…For other shapes, Monte Carlo are more reliable than predictions based on approximate theories. Examples include rods [43][44][45], pentamers [46], tetronimos [47], squares [48][49][50][51][52][53], etc. In three dimensions, the results are much fewer and the detailed phase diagram is known only for long rods [54,55].…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of a system of hard cubes on the cubic lattice

et al. 2019

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We study the phase diagram of a system of 2 × 2 × 2 hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size 2 × L × L where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solid-like sublattice ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size 2 × 2 × L where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters, which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the O(3) universality class perturbed by cubic anisotropy as predicted by the Landau theory.

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Stability of columnar order in assemblies of hard rectangles or squares

Cited by 22 publications

References 67 publications

Columnar-disorder phase boundary in a mixture of hard squares and dimers

Columnar-disorder phase boundary in a mixture of hard squares and dimers

Phase transitions in a system of hard Y-shaped particles on the triangular lattice

Phase diagram of a system of hard cubes on the cubic lattice

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