Monte Carlo approach for studying microphases applied to the axial next-nearest-neighbor Ising and the Ising-Coulomb models

Zhang, Kai

doi:10.1103/physrevb.83.214303

Cited by 15 publications

(18 citation statements)

References 120 publications

(325 reference statements)

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“…It is known that competing short-range attractive and long-range repulsive forces may result in the formation of a diverse variety of patterns [33][34][35][36] . In Sec.…”

Section: The Basic Modelmentioning

confidence: 99%

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Karpov

2016

Phys. Rev. B

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The latest trend in studies of modern electronically and/or optically active materials is to provoke phase transformations induced by high electric fields or by short (femtosecond) powerful optical pulses. The systems of choice are cooperative electronic states whose broken symmetries give rise to topological defects. For typical quasi-one-dimensional architectures, those are the microscopic solitons taking from electrons the major roles as carriers of charge or spin. Because of the longrange ordering, the solitons experience unusual super-long-range forces leading to a sequence of phase transitions in their ensembles: the higher-temperature transition of the confinement and the lower one of aggregation into macroscopic walls. Here we present results of an extensive numerical modeling for ensembles of both neutral and charged solitons in both two-and three-dimensional systems. We suggest a specific Monte Carlo algorithm preserving the number of solitons, which substantially facilitates the calculations, allows to extend them to the three-dimensional case and to include the important long-range Coulomb interactions. The results confirm the first confinement transition, except for a very strong Coulomb repulsion, and demonstrate a pattern formation at the second transition of aggregation.

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“…It is known that competing short-range attractive and long-range repulsive forces may result in the formation of a diverse variety of patterns [33][34][35][36] . In Sec.…”

Section: The Basic Modelmentioning

confidence: 99%

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Karpov

2016

Phys. Rev. B

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“…(The same problem is observed, for instance, in numerical simulations and is similarly solved. [66][67][68] It is interesting to note that in the Z 2 symmetric case (ρ = 1/2) and close to the critical point T ≲ Tc(κ), the equilibrium properties of the lamellar phase found on the anisotropic layered RRG above are the same as for the periodic antiphase found on concentric shells of the Cayley tree in Ref. 41.…”

Section: Inhomogeneous Solutionsmentioning

confidence: 56%

Solution of disordered microphases in the Bethe approximation

Tarzia

2021

The Journal of Chemical Physics

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The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features.Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.

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“…(The same problem is observed, for instance, in numerical simulations and is similarly solved. [62][63][64] It is interesting to note that in the Z 2 symmetric case (ρ = 1/2) and close to the critical point T < ∼ T c (κ), the equilibrium properties of the lamellar phase found on the anisotropic layered RRG above are the same as for the periodic antiphase found on concentric shells of the Cayley tree in Ref. [37].…”

Section: Inhomogeneous Solutionsmentioning

confidence: 58%

Solution of Disordered Microphases in the Bethe approximation

Charbonneau,

Tarzia

2021

Preprint

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The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, as well as between glassiness and microphase ordering.

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Monte Carlo approach for studying microphases applied to the axial next-nearest-neighbor Ising and the Ising-Coulomb models

Cited by 15 publications

References 120 publications

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field

Solution of disordered microphases in the Bethe approximation

Solution of Disordered Microphases in the Bethe approximation

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