Tensionless structure of a glassy phase.

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Computational physics

Background:

• Homogeneous finite-dimensional Ising models have recently demonstrated glassy properties.
• Understanding the nature of excitations in these models is crucial for characterizing their complex behavior.

Purpose of the Study:

• To investigate the scaling of excitation energy with size in 3D Ising models.
• To analyze the role of defects and domain walls in the four-spin model.
• To compare the behavior of 3D and 2D variants of these Ising models.

Main Methods:

• Utilized Monte Carlo simulations to study a specific 3D Ising model.
• Analyzed the energy scaling of large-scale excitations (E(l) ~ l^Theta).
• Examined energy distribution in the four-spin model, focusing on linear defects.

Main Results:

• In a 3D Ising model, the glassy phase under slow cooling is dominated by large-scale excitations with energy scaling exponent Theta ≈ 1.33(20).
• The four-spin model exhibits energy concentrated in linear defects, leading to tensionless domain walls.
• Two-dimensional variants are trivial, with excitation energy likely scaling as Theta=1.

Conclusions:

• The energy scaling of excitations provides insight into the glassy dynamics of these Ising models.
• The presence of tensionless domain walls in the four-spin model is a significant characteristic.
• Dimensionality plays a critical role in the complexity and behavior of these glassy models.