J. Cartes

Simulation of hysteresis for ±J triangular lattices

Abstract We report Monte Carlo simulations of low-temperature hysteresis of ±J Ising triangular lattices. A hysteresis loop similar to the one shown by real spin glasses is found. Such loop is divided in six sectors, according to the coordination number. Average hysteresis curves, obtained over large numbers of randomly prepared samples, are discussed for different values of temperature (T): it is found that the hysteresis loop disappears for T⩾2.2J. Characteristics of the zero-temperature curve are explained by probabilistic analysis.

Hysteresis cycles for

Abstract Hysteresis cycles for cubic ± J Ising spin glasses are obtained by Monte-Carlo simulations and compared to similar results previously reported for triangular systems. Generic characteristics, such as hysteresis cycles divided in sectors and no return memory point, are explained in general. A discussion is done for the magnetization within each sector, dissipated energy per cycle and temperature dependence.

J spin glasses

Ising lattices with ± J interactions and uniform magnetic field are calculated looking for energy, magnetization and correlations at zero temperature. All magnitudes present discontinuities that occur at rational numbers for the magnetic field measured in units of J. We interpret this as a manifestation of pinning due to the complex topology of these lattices.

Discontinuities in ± J Ising lattices

Abstract Two recently introduced order parameters p and h are studied for Ising lattices with competing ferromagnetic and antiferromagnetic interactions. Square, triangular and honeycomb lattices are considered. The results are compared with the traditional order parameters q (Edwards-Anderson) and C R (rigidity), respectively. The advantages of the new magnitudes are brought out.

Order parameters for various Ising lattices with competing ±J interactions

Square Ising lattices with equal amount and equal magnitude of ferromagnetic (F) and antiferromagnetic (AF) exchange interactions (or bonds) are considered. The size is given by the total number of spins N, which is varied. The way in which the N spins are distributed (array) represents the shape of the lattice. We look here for size and shape dependence of parameters characterizing the ground level of these systems: ground state energy per bond e g and site order parameters q, p and h. The results presented below correspond to exact solutions for averages over 500 samples for each kind of array. The computer techniques to perform the calculations are based on partial (or ‘intelligent’) enumeration of the configuration space. We concentrate here on p and h due to their novelty. We present evidence showing that p goes to zero in the thermodynamic limit due to a bimodal distribution, such that the component centered at p = 0 begins to dominate as size increases. On the other hand the single mode distribution for values of h is asymmetric maximizing at about 0.6 and average value of 0.5. The properties of these two distributions become more evident as size grows. The lattices defined only by those bonds that never show frustration (diluted lattices) present a clear tendency to percolate. About 2/3 of the diluted lattices percolate independent of size.

Order Parameters and Percolation for Finite Square Ising Lattices with Mixed Exchange Interactions

Two-dimensional square spin lattices, with Ising Hamiltonian up to nearest-neighbor interactions are considered. The total number of spins (N) defines the size while the shape corresponds to the way of arranging the N spins in a particular rectangular array. Bonds can be either ferromagnetic (−J) or antiferromagnetic (+J), N of each, randomly distributed throughout the lattice. The number of possible distributions of bonds increases rapidly with size. Therefore, a large number (500) of bond distributions (samples) for each size and shape is prepared in order to allow a statistical analysis. For each sample we solve the exact problem looking for ground state properties. It is found that all properties depend strongly on size. Some of them depend also on shape (i.e. ground state energy per bond). In spite of the size limitation due to computer facilities, namely N ≤ 40, it is possible to observe that saturation is clearly present and it is consistent with analytic studies already reported for the thermodynamic limit.