Cyclic annealing as an iterated random map.

Area of Science:

• Condensed matter physics
• Materials science
• Statistical mechanics

Background:

• Disordered magnets, martensitic crystals, and glassy solids exhibit irreversible deformation.
• External deformation induces smooth responses punctuated by abrupt relaxation glitches.

Purpose of the Study:

• To model the evolution of system configurations during deformation-induced glitches.
• To analyze the convergence properties of mapping schemes for disordered systems.

Main Methods:

• Describing system configuration evolution as N-state mappings (U for forward, D for reverse deformation).
• Iterating sequences of maps (e.g., DDDDUUUU) to observe convergence to cyclic state repetitions.
• Employing numerical sampling to characterize convergence properties of four random map types, including the Preisach model.

Main Results:

• Iteration of deformation maps converges to a fixed cyclic repetition of states, often spanning multiple strain cycles.
• The study characterized convergence properties for different random map types with increasing physical restrictions.
• The Preisach model, a highly restrictive map, showed only qualitative resemblance to annealing simulations.

Conclusions:

• A mapping framework can capture the glitch-driven evolution in disordered materials.
• The studied models suggest limitations and highlight properties needed for realistic mapping schemes.
• Further development is required for accurate modeling of irreversible deformation in complex materials.