Glassy and Crystalline States in a Model without Disorder: Spin Analog of a Structural Glass
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in theories of structural glasses such as the curved-space pictures of metallic glass [4]. The two concepts taken together, glassy dynamics in non-random spin systems and frustration as a key to glassy behavior, suggest that frustrated spin systems could play a role in our quest for an understanding of the nature of structural glasses [5]. The model discussed in this paper belongs to this category. It has been shown [6,7] that the frustration of a triangular-lattice Ising antiferromagnet can be removed by elastic distortions. In the deformable lattice, the antiferromagnetic couplings between nearest-neighbor spins depend on their separation. In the simplest model, considered here, only uniform distortions of the lattice are allowed and these are characterized by the relative changes el , e2 and e3 of the three nearest-neighbor bonds lengths. In equilibrium, there is a strong first-order transition from the paramagnetic phase to a "striped" structure. The striped phase has alternating rows of up and down spins and a frozen-in shear distortion with one set of bonds (between parallel spins) expanded and the other two (between antiparallel spins) contracted. Monte Carlo simulations have been used to demonstrate that this picture remains virtually unchanged when fluctuations in bond-lengths are allowed [7]. A strong first-order transition accompanied by a shear distortion is reminiscent of the density functional theory of freezing, where volume change plays a similar role, and it seems natural to ask how the supercooled spin system behaves. Upon quenching the system from the 229 Mat. Res. Soc. Symp. Proc. Vol. 455 ©1997 Materials Research Society
disordered phase to the ordered regime, a phenomenology remarkably similar to structural glasses was observed. Monte Carlo simulations were used to study the dynamics following instantaneous quenches from a high-temperature disordered phase to a range of temperatures below the ordering transition (which was strongly first-order). The dynamics employed was standard spin-exchange dynamics extended to include moves which attempt global changes of the shape and size of the box [7]. These global changes were attempted after a complete sweep of all the spins in the lattice. Three system sizes, 32x32, 48x48 and 64x64 were used to investigate the finite size dependence of physical quantities. DISCUSSION AND RESULTS These simulations lead to an intriguing picture of the supercooled state which could shed some light on the nature of the structural glass transition. Above a certain characteristic temperature, T*, the relaxation of the supercooled state can be described reasonably well
by a stretched exponential behavior although there are some deviations. The time scale for nucleation of the striped phase is extremely long and the system behaves as if it is in equilibrium in the metastable disordered phase. There is a volume change of the lattice but the shear distortion fluctuates around zero, as seen in Fig 1. Fig. 1 also shows the time evolution of the energy per spin. For T > T*, t
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