Strain pseudospins with power-law interactions: Glassy textures of a cooled coupled-map lattice

We consider a spin-1 model of strain pseudospins S(Pr)=0,±1 that arise from a triple-well Landau free energy for a square/rectangle or ``austenite-martensite'' structural transformation of a two-dimensional lattice. The pseudospin model has elastic-compatibility-induced power-law anisotropic (PLA) interactions and no quenched disorder. The iteratively solved local mean-field equations for ⟨S(Pr,t)⟩ form a temperature-dependent PLA-coupled nonlinear-map lattice, where t is the iteration ``time.'' On cooling at a constant rate, the excess entropy shows a weak roll-off near a temperature T=Tg and a sharper elbow at a lower T^, just above a Kauzmann-type TK where the excess entropy would have become negative. The crossover temperatures Tg,T^ decrease logarithmically with cooling rate and mark stability changes in spatiotemporal attractors of the cooled PLA-coupled map. Three phases in ⟨S(Pr,t)⟩ are found, with textures of the martensitic-variant domain walls as ``inherent structures.'' There is a high-temperature (T>Tg) fine scale phase of feathery domain walls and an intermediate temperature (Tg>T>T^) phase of mazelike domain walls, with both showing square-wave oscillations as predominantly period-two attractors but with minority-frequency subharmonic clusters. Finally, there is a low-temperature freezing (T^>T) to a static fixed point or period-one attractor of coarse, irregular bidiagonal twins, as in a strain glass. A Haar-wavelet analysis is used to identify the local attractor dynamics. A central result is that dynamically heterogeneous and mobile low-strain droplets act as catalysts, and can form correlated chains or transient ``catalytic corrals'' to incubate an emerging local texture. The hotspot lifetime vanishes linearly in T-TK, suggesting that TK is a dynamic spinodal limit for generating the ``austenitic'' catalyst, the disappearance of which drives a trapping into one of many bidiagonal glassy states. The model has relevance to martensitic or complex-oxide textures, coupled-map lattices, and configurational-glass transitions.