Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

Magnetism in spin models for depleted honeycomb-lattice iridates: Spin-glass order towards percolation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spin-glass dynamics

Spin glasses are magnetic systems with conflicting and random interactions between the individual spins. The dynamics of spin glasses, as of structural glasses, reflect their complexity. Both in experimental and numerical work the relaxation below the freezing temperature depends strongly on the annealing conditions (aging) and, above the freezing point, relaxation in equilibrium is slow and non-exponential, In this Forum, observed characteristics of the dynamics were summarized and the physical models proposed to explain them were outlined. (C) 1998 Elsevier Science B.V. All rights reserved.

Asymmetric Little spin-Glass model

We study the static properties of the Little model with asymmetric couplings. We show that the thermodynamics of this model coincides with that of the Sherrington-Kirkpatrick model, and we compute the main finite-size corrections to the difference of the free energy between these two models and to some clarifying order parameters. Our results agree with numerical simulations. Numerical results are presented for the symmetric Little model, which show that the same conclusions are also valid in this case.

Asymmetric Little spin-Glass model

We study the static properties of the Little model with asymmetric couplings. We show that the thermodynamics of this model coincides with that of the Sherrington-Kirkpatrick model, and we compute the main finite-size corrections to the difference of the free energy between these two models and to some clarifying order parameters. Our results agree with numerical simulations. Numerical results are presented for the symmetric Little model, which show that the same conclusions are also valid in this case.

The Ground State Energy per Site of the Quantum and Classical Edwards-Anderson Spin Glass in the Thermodynamic Limit

We derive general rigorous lower bounds for the average ground state energy per site e ((d)) of the quantum and classical Edwards-Anderson spin-glass model in dimensions d=2 and d=3 in the thermodynamic limit. For the classical model they imply that e ((2))a parts per thousand yena'3/2 and e ((3))a parts per thousand yena'2.204a <-.

Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter. (C) 2003 American Institute of Physics.

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.