Universality of fluctuation-dissipation ratios: the ferromagnetic model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Critical Phenomena

Background:

• The fluctuation-dissipation ratio (FDR) characterizes the relationship between fluctuations and dissipation in systems out of equilibrium.
• Ising ferromagnets provide a fundamental model for studying phase transitions and critical phenomena.

Purpose of the Study:

• To analytically calculate the FDR for Ising ferromagnets quenched to criticality.
• To investigate the influence of initial conditions and system dimensionality on critical dynamics.
• To clarify the definition and measurement of FDR using local versus global observables.

Main Methods:

• Analytical calculation of the FDR.
• Analysis of long-range and short-range Ising models in the large-dimension limit.
• Comparison of FDR for systems with zero and nonzero initial magnetization.
• Examination of local and global observables for FDR measurement.

Main Results:

• The FDR depends on whether the initial magnetization is zero or nonzero.
• Two distinct classes of critical coarsening dynamics emerge based on initial conditions, each with a unique FDR.
• Global observables are more reliable than local observables for detecting nonequilibrium FDRs in long-range models.

Conclusions:

• Initial conditions critically influence the critical coarsening dynamics and FDR in Ising ferromagnets.
• A clear distinction in FDR behavior is observed for unmagnetized versus initially magnetized systems.
• Global observables offer a robust approach for studying nonequilibrium physics and FDR in complex systems.