Jan-Olov Andersson

Domain growth and thermal relaxation in spin glasses

The low-temperature growth of correlated domains in nearest neighbor Gaussian Ising spin glases in 2, 3 and 4 dimensions is studied by two different Monte Carlo techniques. The first is patterned on the ‘lid’ method previously proposed by the authors. The simulation begins at a low-energy ‘reference’ state which is previously found by annealing, and studies how the system diffuses away from this configuration. The local energy minimum configurations reached in time t during the relaxation at temperature T are analyzed by identifying all the connected clusters of spins which have reversed their initial orientation. In particular, the growth of the average cluster volume is examined. The second approach, which is due to Huse, considers the way in which two replicas of the systems approach a low-energy configuration starting from random and uncorrelated high-energy states. Their time coarse grained magnetizations are compared, yielding a measure of the linear cluster size, again as a function of t and T. All our low-temperature data can be scaled on a master curve, whose abscissa b(t, T) is the line in the t, T plane corresponding to constant cluster volume. The region in which this parametrization exists corresponds to the usual thermodynamical low T phases in 3 and 4D. Within the region the form of the growth laws depends on the dimensionality of the system, and on the type of relaxation. For our method we also find a strong and systematic dependence of the growth laws on the annealing time spent to identify the reference state, which is akin to the aging dependence of the linear response: the longer the annealing time, the slower is the growth.

Equilibrium and nonequilibrium magnetic behaviour of a reentrant Ising spin glass

The reentrant Ising spin glass Fe0.62Mn0.38TiO3 has been investigated using SQUID magnetometry. The system is antiferromagnetic below T(N)(H = 0) = 33 K, and enters a mixed antiferromagnetic/spin glass phase below T(g)(H = 0) = 25.8 K. Within the concept of a recent mean field model, a ratio T(N)(0)/T(g)(0) close to unity indicates both intra- and interlayer frustration. The existence of an overlap length, l(DELTA-T), below which equilibrium spin correlations at temperatures T and T + DELTA-T are indistinguishable has been verified by magnetic relaxation experiments on this spin glass system.

Monte Carlo evidence for the existance of an overlap length in Ising spin glass systems

Abstract Monte Carlo simulations of an Ising spin glass model have been performed. The spin system was qurnched from a random initial condition, equilibrated for a time tw1, whereupon the system was subjected to a field perturbation for a time tw2. After waiting for a time tw3, a weak magnetic field h was applied. The susceptibility χ(t)=(M+(t)−M-(t))/2h, where M±( t) is the magnetisation due to a positive/negative field h, was studied as function. of time. The time dependence of the susceptibility shows behaviour similar to results of temperature cycling experiments. We show, for the first time, that the effects of an overlap length are seen also in field cyclings.

Temperature dependence of free energy barriers in a Cu(7 at. % Mn) spin glass

Time dependent zero-field-cooled magnetisation measurements have been performed in order to determine the temperature dependence of the free energy barriers, B(T), in the spin glass Cu(7 at% Mn). The results have been analysed using the temperature dependence of the free energy barriers predicted in the droplet model, B( T)∝Δ( T) Lψ where L is the size of the droplet. It is found that as T→0 K, Δ (T)→constant, yielding activated dynamics in agreement with the droplet model. As T→ Tg, Δ (T) decreases but stays finite at Tg. This result is in contrast to the current droplet model where Δ (T)→0 when T→ Tg.

Aging behaviour in two- and three-dimensional Ising spin glasses studied by Monte Carlo simulations

Abstract The nonequilibrium character of the spin glass dynamics has been studied in Monte Carlo simulations of two- and three-dimensional short-range Ising spin glass systems. The spin system was quenched in zero field to a temperature T . After equilibrating for a waiting time t w a weak magnetic field was applied and the time dependence of the magnetization M ( t ) was studied. Our results show that the relaxation rate, S ( t ) = ∂M ( t )/ ∂ log t , exhibits a maximum at a time t ≈ t w , which is consistent with results from experiments. If the temperature is increased or decreased prior to the field application, the apparent age t a of the system, as defined by the maximum in relaxation rate, is changed. The results are qualitatively in agreement with experiments as well as with theoretical models for the nonequilibrium spin glass dynamics.