Non-Monotonic Temperature Dependence of Local Dynamics and Local Energy upon Cooling toward the Ising Spin Glass Transition

Abstract

We have performed a detailed analysis of the local dynamics and local energies of the equilibrium, paramagnetic phase of the d = 2 and d = 3 ±J Ising spin glass model. Here we discuss our recently reported observations l) that while the average flip rate and average energy decrease monotonically with decreasing temperature, both the flip rate and energy of an increasing fraction of spins increase as the glass transition is approached on cooling. These findings are consistent with recent experimental results for the frequency-dependent magnetic susceptibility of an insulating spin glass, which showed that the approach to the glass transition could be detected from the high frequency behavior. In an effort to better understand the effects of frustration as the glass transition is approached, and to elucidate recent claims of the presence and ramifications of dynamic heterogeneities significantly above the glass transition temperature Tg in glass-forming materials with self-induced frustration, 2 )- 7 ) we are currently exploring the relationship between microstructure and local dynamics in a variety of systems, including supercooled liquids with self-induced disorder 8 ) and paramagnets with random, quenched disorder. 1 ) In particular, we have recently performed a detailed Monte Carlo simulation study of the paramagnetic phase of the Ising spin glass to characterize the hetero­ geneities induced in this system by the quenched disorder, and to test the model for the emergence of fast processes recently reported in an experimental study of an Ising-like spin glass. 4 ) In the Ising spin glass model, exchange interactions Jij = ±J are fixed randomly to the edges of a lattice, and Ising spins with values <Yi = ±1 are placed on the vertices (sites). Quenched disorder exists in this system due to the random configuration of fixed exchange interactions { Jij}. Because of the presence of frustrated plaquettes (loops along the edges of the lattice in which the product of the exchange interactions around the loop is negative), all the spins cannot satisfy all the interactions simultaneously at any temperature. A glass transition results at temperature T = 1.1 in dimension d = 3 and T = 0 in d = 2. 9 ) Our simulations are performed using the heat-bath Monte Carlo algorithm with periodic boundary conditions for lattices of size 64 2 in d = 2 and 16 3 in d = 3. Depending on T, between 3 x 10 5 and 2 x 10 7 Monte Carlo Steps (MCS) were used to