On the ground-state threshold in random two-dimensional Ising ±J models

For square, triangular, and for hexagonal lattices there is numerical and theoretical support that the ground-state thresholdp _c between ferro- and paramagnetism in random 2D Ising ±J models, withp as the concentration of antiferromagnetic bonds, is identical top ^*which is characterized by minimal matching properties of frustrated plaquettes. From square lattices of size 100×100 we have got p_c,sq<0.117 by simulations which produced average groundstate magnetizations per spin by means of exact minimal matchings. Moreover, from the squareL×L-lattices treated (L = 10, 20, 50, 100) we obtained the estimatep _c,sq 0.1 which is in agreement with the Grinstein estimatep _c,sq 0.099 andp _c,sq 0.105 by Freund and Grassberger.     

Zero- and low-temperature behavior of the two-dimensional ±J Ising spin glass

Scaling arguments and precise simulations are used to study the square lattice ±J Ising spin glass, a prototypical model for glassy systems. Droplet theory explains, and our numerical results show, entropically stabilized long-range spin-glass order at zero temperature, which resembles the energetic stabilization of long-range order in higher-dimensional models at finite temperature. At low temperature, a temperature-dependent crossover length scale is used to predict the power-law dependence on temperature of the heat capacity and clarify the importance of disorder distributions.     

Exact ground states of two-dimensional ±J Ising spin glasses

In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentrationp of negative bonds, withp ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to 1 hr each) for several values ofp. For the ground-state energy of an infinite spin-glass system withp=0.5 we estimateE _0.5 =–1.4015±0.0008. We report on extensive computational tests based on more than 22,000 experiments.     

Metastability of Ising spin chains with nearest—neighbour and next—nearest—neighbour interactions in random fields

One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour and next-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. We consider four cases of the exchange couplings: ferro－ferromagnetic (F－F), ferro－antiferromagnetic (F－AF), antiferro－ferromagnetic (AF－F) and antiferro－antiferromagnetic (AF－AF). The energy minima of chains of no more than 30 spins with periodic boundary conditions are analysed exactly. We found that the average number of energy minima grows exponentially with the number of spins in both cases of RFs. The energy distributions across the corresponding energy minima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weak RF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFs and exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetization averaged over all metastable states decreases logarithmically with the number of spins.     

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.     

Spin-correlation function of the fully frustrated Ising model and ± J Ising spin glass on the square lattice

In this work we study the correlation function of the ground state of two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as correlation function. We estimate the exponent of spin correlation function for fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.     

Magnetic ordering of the bond—diluted two—dimensional mixed spin Ising system

Numerical and analytical results are presented for the magnetic ordering in a bond-diluted spin-1/2 and spin-1 mixed transverse Ising system with a single-ion anisotropy on a honeycomb lattice.Special emphsis is placed on the magnetic ordering under the bond dilution and percolation threshold.We discuss in detail the influence of transverse fields of different sublattics on the normal magnetic ordering and on the magnetic ordering induced by single-lon anisotropy.We find that the magnetic ordering of a system exhibits an explicit difference when receiving the transverse field.This phenomenon has not been revealed in previous reports.     

Two-dimensional Ising model with crossing and four-spin interactions and a magnetic fieldi(π/2)kT

The Ising model on a checkerboard lattice with crossing and four-spin interactions is solved exactly when there is pure imaginary magnetic fieldH=i(/2)kT. The model exhibits a critical point with continuously varying exponents.     

Geometric localization of the threshold in two-dimensional Ising ±J spin glasses forT=0

Following an approach of Toulouse, ground states in random 2D Ising ±J spin glasses (without external magnetic field), on square lattices, and with concentrations 0p0.5 of antiferromagnetic bonds are studied by means of minimal matchings of frustrated plaquettes. Lete(p) be the ground-state energy per spin in the thermodynamic limit. Then the well-known equatione(p)=–2+(p)f(p) holds, wheref(p) is the concentration of frustrated plaquettes and(p) is the average connection length between paired frustrated plaquettes in minimal matchings. Introducing (p) as the probability that a frustrated plaquette is matched to another frustrated plaquette by a connection of length (in a minimal matching), the average length(p) can be rewritten asgl(p)=(p). The study of(p) and its components (p) leads to an intervalp ^*pp ₂ (p ^*0.121±0.008,p ₂0.161±0.008) where the threshold between ferromagnet and paramagnet forT=0 lies. Analyzing a similar so-called adjoined average lengthl(p) admits further insight.     

A simulation of the mixed spin 3–spin 3/2 ferrimagnetic Ising model

The mixed spin 3–spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals ?4 ≤ D_A/J ≤ 8 and ?4 ≤ D_B/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through D_A/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected D_A/J values (?2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α′ = 0, β = 0.125, β′ = 0.875 and γ = γ′ = 1.75).     

Non-equilibrium relaxation study of the ±J Ising model with biquadratic exchange interaction

The spin-1 ±J Ising model with uniform biquadratic couplings on a simple cubic lattice is studied by the Monte Carlo simulation using the non-equilibrium relaxation method. The reentrant phase transition induced by competition between the bilinear and biquadratic couplings is eliminated gradually with increasing randomness of bilinear couplings and disappears entirely in the strong random system. The dynamic exponent of ferromagnetic transition shows non-universal behavior with changing randomness, while this behavior is not observed in the case of staggered quadrupolar transition.     

Reentrant phases in the ± J spin glass

We consider an enlarged phase space of the ±J spin glass which includes the dilute Ising model and the frustrated system. The three orthogonal axes in this space are: (i) The fraction of ferro- to antiferro-magnetic bonds, p; (ii) the ratio of the strengths of the antiferro- to ferromagnetic interacions, q; and (iii) the temperature, T. Within this phase space we observe extended regions of the low-temperature spin-glass phase which is characterized by a unique distribution of the local-order parameter. We observe reentrant phase transitions: for fixed p and q with varying T the distribution of the local order parameter shows paramagnetic, ferromagnetic and then spin-glass phases; for fixed p and T and varying q the distribution shows ferromagnetic to paramagnetic and then spin-glass phases.     

Groundstate threshold in disordered anisotropic +/−J Ising models

In disordered anisotropic square +/− J Ising models SQ(p, q) at groundstates we investigate the pairs (p_c, q_c) of critical concentrations of antiferromagnetic bonds with concentrations p,q, respectively in orthogonal coordinate directions. We are led to p_c(q) ≈ π(q) with π(q) from the so-called adjoined problem. This approach is well supported by simulations for different values of q on the basis of minimal matchings of frustrated plaquettes. In particular, p_c(0) ≈ 0.21 from simulations and π(0) = 0.2113248 …, with the conjecture that p_c(0) = π(0). The concept of the adjoined problem is extended to d-dimensional (hyper-) cubic lattices. We hereby obtain for p_c,d especially in the sotropic case: p_c,3 ≈ 0.154, p_c,4 ≈ 0.170, p_c,5 ≈ 0.178, p_c,6 ≈ 0.182. Moreover, in analogy to SQ(p,q) we used the approach also for honeycomb Ising models HC(p,q,r) with no antiferromagnetic bonds in the third plaquette direction (r = 0).     

Spin Hall effect and spin current generation in two-dimensional systems with random Rashba spin–orbit coupling

We consider a new effect induced by spin–orbit coupling in a two-dimensional electron gas confined in a semiconductor quantum well, i.e. the possibility of spin current generation by fluctuating random Rashba spin–orbit interaction, with the corresponding mean value of the interaction being equal to zero. Our main results suggest that – in contrast to the spatially uniform Rashba spin–orbit interaction – the spin Hall effect does not vanish for typical disorder strengths. We also point out some other possibilities of using such a random Rashba coupling for the generation of spin density and spin current in two-dimensional nonmagnetic structures.     

Quantum communication in spin chains with three-site and Dzyaloshinsky–Moriya interactions

We investigate an arbitrary single-qubit state transfer through spin chains with three-site and Dzyaloshinsky–Moriya interactions as well as the quantum discord transfer through double independent spin chains. It is shown that both the three-site and Dzyaloshinsky–Moriya interactions can improve the transfer quality in some cases and the influence of a combination of the three-site and Dzyaloshinsky–Moriya interactions is not simply a linear addition of each contribution. We also find that the three-site coupling may enhance the maximum discord more obviously while the Dzyaloshinsky–Moriya coupling may accelerate the maximum discord more effectively. Furthermore, we show that the quantum discord can always be transferred while the quantum entanglement has a threshold of minimum entanglement to be transferred and may experience entanglement sudden birth and death or even never receive any entanglement for some initial states.     

Dynamic magnetic behavior of the mixed spin （2, 5/2） Ising system with antiferromagnetic/antiferromagnetic interactions on a bilayer square lattice

Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin （2, 5/2） Ising system for the antiferromagnetic/antiferromagnetic （AFM/AFM） interactions on the bilayer square lattice under a time varying （sinusoidal） magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic （FM/FM） and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions.     

Cumulants in the 3-dimensional Ising,O（2） and O（4） spin models

Based on the universal properties of a critical point in different systems and that the QCD phase transitions fall into the same universality classes as the 3-dimensional Ising, O（2） or O（4） spin models, the critical behavior of cumulants and higher cumulant ratios of the order parameter from the three kinds of spin models is studied. We found that all higher cumulant ratios change dramatically the sign near the critical temperature. The qualitative critical behavior of the same order cumulant ratio is consistent in these three models.     

Ising model with competing “uncle–nephew” interactions

ABSTRACT

We consider the Ising model on the semi-infinite Cayley tree of second order with competing interactions up to the third-nearest-neighbors with spins belonging to the different branches of the tree and for this model investigate the problem of phase transition.