Bimodal and Gaussian Ising spin glasses in dimension two

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Physics

Background:

• Ising spin glasses (ISGs) are fundamental models in statistical mechanics.
• Understanding their phase transitions, especially at zero temperature, is crucial.
• Distinguishing between different interaction distributions (bimodal vs. Gaussian) is key to characterizing their behavior.

Purpose of the Study:

• To analyze numerical simulation data for Ising spin glasses with bimodal and Gaussian interactions.
• To determine and compare critical exponents (η and ν) for both models at zero temperature.
• To investigate the influence of interaction distribution on the thermodynamic limit behavior.

Main Methods:

• Numerical simulations on L=128 square lattice Ising spin glasses.
• Analysis using conventional (T) and specialized (τ(b)) scaling variables.
• Extrapolation of simulation data for susceptibility (χ) and correlation length (ξ) to the critical limit (τ(b)=0).

Main Results:

• Gaussian ISGs yield critical exponents η=0 and ν=3.55(5), consistent with literature.
• Bimodal ISGs exhibit distinct critical exponents η=0.20(2) and ν=4.8(3).
• A crossover temperature T(*)(L) distinguishes energy level regimes in bimodal ISGs, vanishing in the thermodynamic limit.

Conclusions:

• The interaction distribution significantly impacts critical behavior in Ising spin glasses.
• Bimodal ISGs possess unique zero-temperature critical properties distinct from Gaussian ISGs.
• The specialized scaling variable τ(b) is effective for analyzing zero-temperature transitions in ISGs.