We consider the two-dimensional randomly site diluted Ising model and the random-bond +-J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder. Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation threshold of the lattice is characterized by unconventional activated (exponential) dynamical scaling and strong Griffiths effects. We calculate the critical behavior in two and three space dimensions, and we also relate our results to the recently found infinite-randomness fixed point in the disordered one-dimensional contact process.
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.
The site-diluted transverse field Ising model in two dimensions is studied with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the transverse field (Gamma) and temperature (T) plane for various (fixed) concentrations (p). The nature of the quantum Griffiths phase at zero temperature is investigated by calculating the distribution of the local zero-frequency susceptibility. It is pointed out that the nature of the Griffiths phase is different for small and large Gamma.
Glauber dynamics of a bond-diluted Ising model on a Bethe lattice (a random graph with fixed connectivity) is investigated by an approximate theory which provides exact results for equilibrium properties. The time-dependent solutions of the dynamical system derived by this method are in good agreement with the results obtained by Monte Carlo simulations in almost all situations. Furthermore, the derived dynamical system exhibits a remarkable phenomenon that the magnetization shows multi-step relaxations at intermediate time scales in a low-temperature part of the Griffiths phase without bond p…
We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dyn…
In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in $d = 3$--5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In $d = 4$ and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d = 4$ is conf…
We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a s…
Large-scale Monte Carlo simulations of the bond-diluted three-dimensional 4-state Potts model are performed. The phase diagram and the physical properties at the phase transitions are studied using finite-size scaling techniques. Evidences are given for the existence of a tricritical point dividing the phase diagram into a regime where the transitions remain of first order and a second regime where the transitions are softened to continuous ones by the influence of disorder. In the former regime, the nature of the transition is essentially clarified through an analysis of the energy probabilit…
We revisited, by means of numerical simulations, the one dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean field theories. In these models the probability that two spins at distance $r$ interact (via a disordered interactions, $J_{ij}=\pm 1$) decays as $r^{-ρ}$. We have estimated, using finite size scaling techniques, the infinite volume correlation length and spin glass susceptibility for $ρ=5/3$ and $ρ=9/5$. We have obtained strong evidence for divergences of the previous observables at a non zero critical temperature. We discuss the behavior of the criti…
We have calculated analytically the mean value and the variance of the number of bonds on the lattices of dimension $d$ for the given occupation of sites. We consider both kinds of site occupation: with the fixed concentration $n_s$ of occupied sites and with the probability $p$ for a site to be occupied. We found that the variance are smaller in the former case and not depends from the dimensionality of the hypercubic lattice. Whereas in the last case it grows with the space dimensionality. The ratio of variances are quite different in the limit of $p\to 1$. Finally, we demonstrate the releva…
We derive high-temperature series expansions for the free energy and the susceptibility of random-bond $q$-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength $p$ as well as the dimension $d$ as symbolic parameters. By applying several series analysis techniques to the new series expansions, one can scan large regions of the $(p,d)$ parameter space for any value of $q$. For the bond-diluted 4-state P…
Frequency evolutions of hysteresis loop area and hysteresis tools such as remanence and coercivity of a kinetic Ising model in the presence of quenched bond dilution are investigated in detail. The kinetic equation describing the time dependence of the magnetization is derived by means of effective-field theory with single-site correlations. It is found that the frequency dispersions of hysteresis loop area, remanence and coercivity strongly depend on the quenched bond randomness, as well as applied field amplitude and oscillation frequency. In addition, the shape of the hysteresis curves for …
This is a reply to the comment by A. W. Sandvik (cond-mat/0010433) on our paper Phys. Rev. Lett. 84, 4204 (2000). We show that his data do not conflict with our data nor with our conclusions.
In this report we give an overview on recent results obtained from extensive Monte Carlo (MC) computer simulations of the 3D 2-state (Ising) and 4-state Potts models with bond-dilution. The motivation to study the 4-state Potts model derives from the fact that, in the pure case, this model is known to exhibit a fairly strong first-order transition, such that a disorder-induced softening to a second-order transition would give clear support of the theoretical expectations. Modeling the disorder by bond-dilution enables in the Ising case a test of the expected universality with respect to the ty…
Recently, a method has been proposed to obtain accurate predictions for low-temperature properties of lattice spin glasses that is practical even above the upper critical dimension, $d_c=6$. This method is based on the observation that bond-dilution enables the numerical treatment of larger lattices, and that the subsequent combination of such data at various bond densities into a finite-size scaling Ansatz produces more robust scaling behavior. In the present study we test the potential of such a procedure, in particular, to obtain the stiffness exponent for the hierarchical Migdal-Kadanoff l…
We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution p*, at which a spin glass (SG) phase appears, lies in the sa…
The influence of random site dilution on the critical properties of the two-dimensional Ising model on a square lattice was explored by Monte Carlo simulations with the Wang-Landau sampling. The lattice linear size was $L = 20-120$ and the concentration of diluted sites $q=0.1, 0.2, 0.3$. Its pure version displays a second-order phase transition with a vanishing specific heat critical exponent $α$, thus, the Harris criterion is inconclusive, in that disorder is a relevant or irrelevant perturbation for the critical behavior of the pure system. The main effort was focused on the specific heat a…
Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.
A spin-glass transition occurs both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Using different finite size scaling methods evidence for a spin-glass transition is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field. The application of a new…
The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random bond dilution is studied using quantum Monte Carlo simulation at the percolation threshold (50% of the bonds removed). Finite-size scaling of the staggered structure factor averaged over the largest connected clusters of sites on L*L lattices shows that long-range order exists within the percolating fractal clusters in the thermodynamic limit. This implies that the order-disorder transition driven by bond-dilution occurs exactly at the percolation threshold and that the exponents are classical. This result should apply al…
We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corr…
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 conn…
The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one condensed pattern. We derive restrictions on the storage capacity and the mutual information content occuring during the retrieval process. Special focus is on the constraints on the threshold for optimal performance. We also look at the effect of noisy updating, giving a dynamical version of the critical temperature, the corresponding threshold and an approximat…
We use numerical simulations and an effective-medium theory to study the rigidity percolation transition of the honeycomb and diamond lattices when weak bond-bending forces are included. We use a rotationally invariant bond-bending potential, which, in contrast to the Keating potential, does not involve any stretching. As a result, the bulk modulus does not depend on the bending stiffness $κ$. We obtain scaling functions for the behavior of some elastic moduli in the limits of small $Δ\mathcal{P} = 1 - \mathcal{P}$, and small $δ\mathcal{P} = \mathcal{P} - \mathcal{P}_c$, where $\mathcal{P}$ is…
We have successfully grown sizable single crystals of La_2Cu_{1-z}(Zn,Mg)_zO_4 with up to nearly half of the magnetic Cu sites replaced by non-magnetic Zn and Mg. Neutron scattering, SQUID magnetometry, and complementary quantum Monte Carlo (QMC) simulations demonstrate that this material is an excellent model system for the study of site percolation of the square-lattice Heisenberg antiferromagnet (SLHAF) in the quantum-spin limit S=1/2. Carefully oxygen-reduced samples exhibit Neel order up to the percolation threshold for site dilution, z_p ~ 40.7%. Up to at least z = 35%, the Neel temperat…
We investigate quantum phase transitions in the spin-1/2 Heisenberg antiferromagnet on square lattices with inhomogeneous bond dilution. It is shown that quantum fluctuations can be continuously tuned by inhomogeneous bond dilution, eventually leading to the destruction of long-range magnetic order on the percolating cluster. Two multicritical points are identified at which the magnetic transition separates from the percolation transition, introducing a novel quantum phase transition. Beyond these multicritical points a quantum-disordered phase appears, characterized by an infinite percolating…
Bond-dilution effects on spin-1/2 spin-gapped Heisenberg antiferromagnets of coupled alternating chains on a square lattice are investigated by means of the quantum Monte Carlo method. It is found that, in contrast with the site-diluted system having an infinitesimal critical concentration, the bond-diluted system has a finite critical concentration of diluted bonds, $x_{c}$, above which the system is in an antiferromagnetic (AF) long-range ordered phase. In the disordered phase below $x_{c}$, plausibly in the concentration region significantly less than $x_{c}$, the system has a spin gap due …
In Phys. Rev. Lett. 84, 4204 (2000) (cond-mat/9905379), Kato et al. presented quantum Monte Carlo results indicating that the critical concentration of random non-magnetic sites in the two-dimensional antiferromagnetic Heisenberg model equals the classical percolation density; pc=0.407254. The data also suggested a surprising dependence of the critical exponents on the spin S of the magnetic sites, with a gradual approach to the classical percolation exponents as S goes to infinity. I here argue that the exponents in fact are S-independent and equal to those of classical percolation. The appar…
We report on large-scale Monte Carlo simulations of the three-dimensional 4-state Potts ferromagnet subject to quenched, random bond dilution. For small dilutions the rather strong first-order phase transition of the pure system is found to persist, whereas for larger dilutions the theoretically expected softening to a continuous transition is confirmed. The properties of the underlying disorder distributions of thermal observables are discussed and illustrated with a few selected examples.
The non-equilibrium dynamics of the strongly diluted random-bond Ising model in two-dimensions (2d) is investigated numerically. The persistence probability, P(t), of spins which do not flip by time t is found to decay to a non-zero, dilution-dependent, value $P(\infty)$. We find that $p(t)=P(t)-P(\infty)$ decays exponentially to zero at large times. Furthermore, the fraction of spins which never flip is a monotonically increasing function over the range of bond-dilution considered. Our findings, which are consistent with a recent result of Newman and Stein, suggest that persistence in disorde…
We study by Monte Carlo simulations the influence of bond dilution on the three-dimensional Ising model. This paradigmatic model in its pure version displays a second-order phase transition with a positive specific heat critical exponent $α$. According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, between the pure model limit and the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrate…
We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, wh…
By tempered Monte Carlo simulations, we study 2D site-diluted dipolar Ising systems. Dipoles are randomly placed on a fraction x of all L^2 sites in a square lattice, and point along a common crystalline axis. For x_c< x<=1, where x_c = 0.79(5), we find an antiferromagnetic phase below a temperature which vanishes as x approaches x_c from above. At lower values of x, we study (i) distributions of the spin--glass (SG) overlap q, (ii) their relative mean square deviation Delta_q^2 and kurtosis and (iii) xi_L/L, where xi_L is a SG correlation length. From their variation with temperature and syst…
Classical and quantum conduction on a bond-diluted Bethe lattice is considered. The bond dilution is subject to the constraint that every occupied bond must have at least $k-1$ neighboring occupied bonds, i.e. $k$-core diluted. In the classical case, we find the onset of conduction for $k=2$ is continuous, while for $k=3$, the onset of conduction is discontinuous with the geometric random first-order phase transition driving the conduction transition. In the quantum case, treating each occupied bond as a random scatterer, we find for $k=3$ that the random first-order phase transition in the ge…
Dilution effects on spin-1/2 quantum Heisenberg antiferromagnets with a non-magnetic spin-gapped ground state are studied by means of the qunatum Monte Carlo simulation. In the site-diluted system, an antiferromagnetic long-range order (AF-LRO) is induced at an infinitesimal concentration of dilution due to an effective coupling $\tilde{J}_{mn}$ between induced magnetic moments. In the bond-diluted case, on the other hand, the AF-LRO is not induced up to a certain concentration of dilution due to singlet pairs reformed by an AF coupling $\tilde{J}_{\rm af}$ between the edge spins of the dilute…
The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming ac…
The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed inter-layer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multi-critical point (p*,g*) at the classical percolation density p=p* and inter-layer coupling g* approximately 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero inter-layer coupling and could be relevant for antiferromagnetic cuprates doped with non-magnetic impurities.
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 wi…
In a diluted magnetic semiconductor system, the exchange interaction between magnetic impurities has two independent components: a direct antiferromagnetic interaction and a ferromagnetic interaction mediated by charge carriers. Depending on the system parameters, the ground state of the system may be ordered either ferromagnetically or randomly. In this paper we use percolation theory to find the ferromagnetic transition temperature and the location of the quantum critical point separating the ferromagnetic phase and a valence bond glass phase.
We present a numerical study of ground states of the dilute versions of the Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called "sparse" mean-field spin glasses that have been studied widely on random networks of finite (average or regular) degree, the networks studied here are randomly bond-diluted to an overall density $p$, such that the average degree diverges as $\sim pN$ with the system size $N$. Ground-state energies are obtained with high accuracy for random instances over a wide range of fixed $p$. Since this is a NP-hard combinatorial problem, we employ the Ex…
We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griff…
We present a theoretical study of diluted magnetic semiconductors that includes spin-orbit coupling within a realistic host band structure and treats explicitly the effects of disorder due to randomly substituted Mn ions. While spin-orbit coupling reduces the spin polarization by mixing different spin states in the valence bands, we find that disorder from Mn ions enhances the spin polarization due to formation of ferromagnetic impurity clusters and impurity bound states. The disorder leads to large effects on the hole carriers which form impurity bands as well as hybridizing with the valence …
We present a large-scale simulation of the ground state interface properties of the diluted Sherrington-Kirkpatrick spin glass of Gaussian disorder for a broad range of the bond occupation probability $p$ using the strong disorder renormalization group and the population annealing Monte Carlo methods. We find that the interface is space-filling independent of $p$, i.e., the fractal dimension $d_s=1$. The stiffness exponent $θ$ is likely also independent of $p$, despite that the energy finite-size correction exponent $ω$ varies with $p$ as recently found. The energy finite-size scaling is also …
We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder averaged persistence probability $\bar{{P}_c}(t)$ of the global magnetization is found to decay algebraically with an exponent $θ_c$ that we compute analytically in a dimensional expansion in $d=4-ε$. Corrections to Markov process are found to occur already at one loop order and $θ_c$ is thus a novel exponent characterizing this disordered critical point. Our result is thoroughly compared with Monte Carlo simulations in $d=3$, which also include a measurement…
By tempered Monte Carlo simulations, we study site-diluted Ising systems of magnetic dipoles. All dipoles are randomly placed on a fraction x of all L^3 sites of a simple cubic lattice, and point along a given crystalline axis. For x_c< x<=1, where x_c = 0.65, we find an antiferromagnetic phase below a temperature which vanishes as x tends to x_c from above. At lower values of x, we find an equilibrium spin-glass (SG) phase below a temperature given by k_B T_{sg} = x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy. We study (a) the relative mean square deviation D_q^2 of …
We present an effective medium theory that includes bending as well as stretching forces, and we use it to calculate mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability $p$. We find a rigidity threshold $p_b$ which has the same value for all positive bending rigidity and a crossover characterizing bending-, stretching-, and bend-stretch coupled elastic regimes controlled by…
We examine the stability of magnetic order in a classical Heisenberg model with quenched random exchange couplings. This system represents the spin degrees of freedom in high-$T_\textrm{c}$ compounds with immobile dopants. Starting from a replica representation of the nonlinear $σ$-model, we perform a renormalization-group analysis. The importance of cumulants of the disorder distribution to arbitrarily high orders necessitates a functional renormalization scheme. From the renormalization flow equations we determine the magnetic correlation length numerically as a function of the impurity conc…
The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random site dilution is studied using quantum Monte Carlo simulations. Ground state properties of the largest connected cluster on L*L lattices, with L up to 64, are calculated at the classical percolation threshold. In addition, clusters with a fixed number Nc of spins on an infinite lattice at the percolation density are studied for Nc up to 1024. The disorder averaged sublattice magnetization per spin extrapolates to the same non-zero infinite-size value for both types of clusters. Hence, the percolating clusters, which are f…
We report a numerical study of the bond-diluted 2-dimensional Potts model using transfer matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one observed in the random bond case, confirming the general picture according to which a unique fixed point des…
The recently proposed reduction method for diluted spin glasses is investigated in depth. In particular, the Edwards-Anderson model with \pm J and Gaussian bond disorder on hyper-cubic lattices in d=2, 3, and 4 is studied for a range of bond dilutions. The results demonstrate the effectiveness of using bond dilution to elucidate low-temperature properties of Ising spin glasses, and provide a starting point to enhance the methods used in reduction. Based on that, a greedy heuristic call ``Dominant Bond Reduction'' is introduced and explored.
The three-dimensional Edwards-Anderson spin-glass model present strong spatial heterogeneities well characterized by the so-called backbone, a magnetic structure that arises as a consequence of the properties of the ground state and the low-excitation levels of such a frustrated Ising system. Using extensive Monte Carlo simulations and finite size scaling, we study how these heterogeneities affect the phase transition of the model. Although, we do not detect any significant difference between the critical behavior displayed by the whole system and that observed inside and outside the backbone,…
We present several different calculations pertaining to the nature of the low-energy excitations of the site-diluted S=1/2 Heisenberg antiferromagnet, in particular at the percolation point. We present a picture of excitations originating from an effective low-energy subsystem consisting of localized magnetic moments. At the percolation point, these moments lead to an anomalously large dynamic exponent; z=3.6(1). The magnetic moments are shown to originate from local sublattice imbalance, which we study quantitatively using a classical dimer-monomer model. The localization properties of triple…
We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin-glass models: the +-J Ising model for two values of the disorder parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for bond-occupation probability p_b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent omega related to the leading irrelevant operator, omega=1.0(1). We also determine the critical exponents nu and eta. Taking into a…
The random-bond Ising model on the square lattice has several disordered critical points, depending on the probability distribution of the bonds. There are a finite-temperature multicritical point, called Nishimori point, and a zero-temperature fixed point, for both a binary distribution where the coupling constants take the values +/- J and a Gaussian disorder distribution. Inclusion of dilution in the +/- J distribution (J=0 for some bonds) gives rise to another zero-temperature fixed point which can be identified with percolation in the non-frustrated case (J >= 0). We study these fixed poi…
We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin-glass models on cubic lattices of size L: the +- J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p=0.5 and p=0.7 (up to L=28 and L=20, respectively), and the bond-diluted bimodal model for bond-occupation probability p_b = 0.45 (up to L=16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent ωrelated to the…
