Nonequilibrium critical dynamics of the two-dimensional ±J Ising model

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Information

Background:

• The ±J Ising model is a frustrated spin system with applications in quantum error correction.
• Understanding its nonequilibrium critical behavior is crucial for complex systems.

Purpose of the Study:

• Investigate the nonequilibrium critical dynamics of the 2D ±J Ising model after a quench to its critical point.
• Analyze the behavior across the paramagnetic-ferromagnetic transition line, including the Nishimori point.

Main Methods:

• Simulations of the two-dimensional ±J Ising model under critical quenches.
• Analysis of the dynamical critical exponent (z_c) and spin cluster geometry.
• Characterization using stochastic Loewner evolution (SLE).

Main Results:

• Nonuniversal dynamical critical exponent (z_c) observed for quenches above and below the Nishimori point (NP).
• Asymptotic regime with z_c ≃ 6.02(6) reached for quenches directly to the NP.
• Emergent critical percolation topology observed at large length scales for quenches from the paramagnetic phase.

Conclusions:

• The ±J Ising model exhibits distinct nonequilibrium critical behaviors depending on the quench conditions relative to the Nishimori point.
• Stochastic Loewner evolution effectively characterizes universality classes.
• A universal emergent percolation topology is found, independent of frustration.