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Register a new userCrossover effects in the bond-diluted Ising model in three dimensions
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P.E. Berche
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We investigate by Monte Carlo simulations the critical properties of the three-dimensional bond-diluted Ising model. The phase diagram is determined by locating the maxima of the magnetic susceptibility and is compared to mean-field and effective-medium approximations. The calculation of the size-dependent effective critical exponents shows the competition between the different fixed points of the model as a function of the bond dilution.
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We study the $pm J$ three-dimensional Ising model with a spatially uniaxially anisotropic bond randomness on the simple cubic lattice. The $pm J$ random exchange is applied in the $xy$ planes, whereas in the z direction only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied, at the ferromagnetic-paramagnetic transition line, using parallel tempering and a convenient concentration of antiferromagnetic bonds ($p_z=0 ; p_{xy}=0.176$). The numerical data point out clearly to a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3d random Ising model. The smooth finite-size behavior of the effective exponents describing the peaks of the logarithmic derivatives of the order parameter provides an accurate estimate of the critical exponent $1/ u=1.463(3)$ and a collapse analysis of magnetization data gives an estimate $beta/ u=0.516(7)$. These results, are in agreement with previous studies and in particular with those of the isotropic $pm J$ three-dimensional Ising at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.
We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the occupation concentration p of the disordered cluster, the size of the underlying lattice, and the type of connection chosen between the cluster and the input and output leads. We investigate both the point-to-point contacts and the busbar type of connection. For highly diluted clusters we find the behavior of the transmission to be independent of the type of connection. As the amount of dilution is decreased we find sharp variations in transmission. These variations are the remnants of the resonances at the ordered, zero-dilution, limit. For particles with energies within 0.25 <= E <= 1.75 (relative to the hopping integral) and with underlying square lattices of size 20x20, the configurations begin transmitting near p_a = 0.60 with T against p curves following a common pattern as the amount of dilution is decreased. Near p_b = 0.90 this pattern is broken and the transmission begins to vary with the energy. In the asymptotic limit of very large clusters we find the systems to be totally reflecting except when the amount of dilution is very low and when the particle has energy close to a resonance value at the ordered limit or when the particle has energy at the middle of the band.
Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a site-diluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction x of all L^3 sites of a simple cubic lattice that point up or down along a given crystalline axis. For x < 0.65 these systems are known to exhibit an equilibrium spin-glass phase below a temperature T_sg proportional to x. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter q that are strongly sample-dependent. We focus on spikes associated with large excitations. From cumulative distributions of q and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with L. This is compared with the behaviour found for the Sherrington-Kirkpatrick model.
We investigate and contrast, via entropic sampling based on the Wang-Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied and their general universality aspects are inspected by a detailed finite-size scaling (FSS) analysis. We find that, the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties for a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. Yet, a careful FSS analysis of our data favors the field-theoretically predicted logarithmic corrections.
The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to test for logarithmic corrections to pure power-law decay against distance. Fits of our data to conformal-invariance expressions, specific to logarithmic corrections to correlations on strips, give results with the correct sign, for the moments of order $n=0-4$ of the correlation-function distribution. We find an interval of disorder strength along which corrections to pure-system behavior can be decomposed into the product of a known $n$-dependent factor and an approximately $n$-independent one, in accordance with predictions. A phenomenological fitting procedure is proposed, which takes partial account of subdominant terms of correlation-function decay on strips. In the low-disorder limit, it gives results in fairly good agreement with theoretical predictions, provided that an additional assumption is made.
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