Evidence that the de Almeida-Thouless transition disappears below six dimensions.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Disordered Systems

Background:

• Parisi's broken replica symmetry theory predicts a phase transition in spin glasses at the de Almeida-Thouless (AT) line.
• This transition occurs in the h-T plane under an applied magnetic field.

Purpose of the Study:

• Investigate the AT line in power-law diluted Heisenberg spin glasses.
• Determine the validity of Parisi's theory in lower dimensions.

Main Methods:

• Numerical simulations of Heisenberg spin glasses with power-law interactions (1/r^{2σ}).
• Analysis of the AT line in the presence of a random vector field.
• Relating the exponent σ to the effective dimension d=2/(2σ-1).

Main Results:

• The squared AT line field scales as h_{AT}^{2}∼(2/3-σ).
• The AT line is found to not exist for dimensions below six.
• The phase transition falls within the universality class of Ising spin glasses in a field.

Conclusions:

• Parisi's theory, specifically the AT line, is not appropriate for spin glasses in three dimensions.
• The findings challenge the universality of the Parisi scheme in lower-dimensional systems.