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

Abstract

We consider a spin-1 model of strain pseudospins S(r^→)=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(r^→,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=T_g and a sharper elbow at a lower T, just above a Kauzmann-type T_K where the excess entropy would have become negative. The crossover temperatures T_g,T decrease logarithmically with cooling rate and mark stability changes in spatiotemporal attractors of the cooled PLA-coupled map. Three phases in <S(r^→,t)> are found, with textures of the martensitic-variant domain walls as “inherent structures.” There is a high-temperature (T>T_g) fine scale phase of feathery domain walls and an intermediate temperature (T_g>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-T_K, 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.