Lower-critical spin-glass dimension from 23 sequenced hierarchical models

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Computational physics

Background:

• The Ising spin-glass phase is a complex state of magnetic matter.
• Understanding its critical dimensions is key to theoretical models.
• Hierarchical lattices offer a tractable model system for studying phase transitions.

Purpose of the Study:

• To numerically determine the lower-critical dimension (dL) for the Ising spin-glass phase.
• To investigate the behavior of phase transition temperatures and critical exponents in these systems.
• To provide an accurate value for dL in a specific class of lattices.

Main Methods:

• Numerical calculation of the phase transition temperature (T) and critical exponents (yT, yR).
• Utilizing a family of hierarchical lattices with varying fractional dimensions.
• Employing a near-linear fit with a high correlation coefficient (R2=0.999999) to extrapolate results.

Main Results:

• The lower-critical dimension (dL) was calculated to be 2.520.
• The study achieved essentially exact results through precise fitting.
• Phase transition temperature and runaway exponents were determined for multiple lattice dimensions.

Conclusions:

• The calculated lower-critical dimension of 2.520 provides a precise benchmark for Ising spin-glass models.
• The methodology offers a robust approach for determining critical dimensions in complex systems.
• This finding advances the understanding of disordered magnetic phases in condensed matter physics.