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Tiling the plane without supersymmetry

Bazeia¹, Brito

¹Departamento de Fisica, Universidade Federal da Paraiba, Caixa Postal 5008, 58051-970 Joao Pessoa, Paraiba, Brazil.

Physical Review Letters

|October 4, 2000

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Researchers have developed a stable, hexagonal network of defects using a Z3 symmetric model. This defect network, formed by three-junctions, tiles the plane without requiring supersymmetry.

Area of Science:

Theoretical physics
Condensed matter physics

Background:

Defect networks are crucial in understanding phase transitions and material properties.
Symmetry principles, such as Z3 symmetry, often dictate the formation and stability of such networks.

Purpose of the Study:

To introduce a novel method for tiling the plane with a regular hexagonal network of defects.
To demonstrate the stability and formation mechanism of this network based on Z3 symmetry.

Main Methods:

Utilizing a theoretical model involving two real scalar fields with Z3 symmetry.
Analyzing the stability of the network through the properties of three-junctions.

Main Results:

A stable, regular hexagonal network of defects has been successfully constructed.

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The network's stability is a direct consequence of the three-junctions inherent in the Z3 symmetric model.

Conclusions:

The Z3 symmetry is fundamental to the formation and stability of the hexagonal defect network.
This approach provides a mechanism for creating ordered defect structures without invoking supersymmetry.