Triangles on a triangular lattice: Insights into self-assembly in two dimensions driven by shape complementarity

Akimenko, S. S.; Myshlyavtsev, A. V.; Myshlyavtseva, M. D.; Горбунов, В. А.; Podgornyi, S. O.; Solovyeva, O. S.

doi:10.1103/physreve.105.044104

Cited by 5 publications

(9 citation statements)

References 71 publications

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“…The 1-NN model shows a single continuous transition, belonging to the Ising universality class, from a fluid to a sublattice-ordered phase. The 2-NN model shows a first-order transition, while the 3-NN model, surprisingly, does not undergo any transition [49,50]. The 4-NN model shows a single continuous phase transition that belongs to the three-state Potts model.…”

Section: Introductionmentioning

confidence: 91%

“…On the honeycomb lattice, the model has been studied for k 5 [49][50][51]. The 1-NN model shows a single continuous transition, belonging to the Ising universality class, from a fluid to a sublattice-ordered phase.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, there have been two other algorithms that have proved useful. One is the TRG method, which was used to obtain the phase diagram for the k-NN model on the triangular lattice for k 5 [55] and interacting hard equilateral triangles [50]. The other is the strip cluster Wang-Landau (SCWL) algorithm that combines the SCUA with flat histogram methods and thus determines the density of states for all densities [56,62].…”

Section: Introductionmentioning

confidence: 99%

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Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor

et al. 2022

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Hard-core lattice-gas models are minimal models to study entropy-driven phase transitions. In the k-nearestneighbor lattice gas, a particle excludes all sites up to the kth next-nearest neighbors from being occupied by another particle. As k increases from one, it extrapolates from nearest-neighbor exclusion to the hard-sphere gas. In this paper we study the model on the triangular lattice for k 7 using a flat histogram algorithm that includes cluster moves. Earlier studies focused on k 3. We show that for 4 k 7, the system undergoes a single phase transition from a low-density fluid phase to a high-density sublattice-ordered phase. Using partition function zeros and nonconvexity properties of the entropy, we show that the transitions are discontinuous. The critical chemical potential, coexistence densities, and critical pressure are determined accurately.

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor

et al. 2022

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“…In the first approximation, the outcome of self-assembly of equilibrium nanostructures is determined by the shape of the building blocks-molecules and nanoparticles [1][2][3][4]. The self-assembly of 'rigid' particles is primarily influenced by the entropy contribution and usually leads to the formation of dense structures [5][6][7][8][9][10]. The functionalization of organic molecules [11][12][13][14] and colloidal particles [2,[15][16][17][18][19][20] introduces specific lateral interactions, leading to more complex and not close-packed phases.…”

Section: Introductionmentioning

confidence: 99%

“…To date, the phase behavior of monolayers of rigid noninteracting particles of various shapes has been extensively studied. Among them are disks [22][23][24][25][26][27][28][29], triangles [10,[30][31][32], squares [33][34][35][36][37][38][39][40], and others.…”

Section: Introductionmentioning

confidence: 99%

Shape-interaction dualism: unraveling complex phase behavior in triangular particle monolayers

Akimenko,

Gorbunov,

Myshlyavtsev

et al. 2024

J. Phys.: Condens. Matter

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This paper examines the effect of finite attractive and repulsive interactions on the self-assembly of triangular-shaped particles on a triangular lattice. The ground state analysis of the lattice model has revealed an infinite sequence of ordered structures, a phenomenon referred to as the "devil's staircase" of phase transitions. The model has been studied at finite temperatures using both the transfer-matrix and tensor renormalization group methods. The concurrent use of these two methods lends credibility to the obtained results. It has been demonstrated that the initial ordered structures of the "devil's staircase" persist at non-zero temperatures. Further increase of the attraction between particles or a decrease of the temperature induces the appearance of subsequent ordered structures of the "devil's staircase". The corresponding phase diagram of the model has been calculated. The phase behavior of our model agrees qualitatively with the phase behavior of trimesic acid adsorption layer on single crystal surfaces.

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Equilibrium structure of 1,4-cyclohexadiene monolayer on Si(001)-(2 × 1)

Gorbunov,

Uliankina,

Akimenko

et al. 2024

Phys. Rev. B

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Triangles on a triangular lattice: Insights into self-assembly in two dimensions driven by shape complementarity

Cited by 5 publications

References 71 publications

Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor

Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor

Shape-interaction dualism: unraveling complex phase behavior in triangular particle monolayers

Equilibrium structure of 1,4-cyclohexadiene monolayer on Si(001)-(2 × 1)

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