Ising Spin-Based Error Correcting Private-Key Cryptosystems

Ising spin system has been shown to provide a new class of error-correction code and can be used to construct public-key cryptosystems by making use of statistical mechanics. The relation between Ising spin systems and private-key cryptosystems are investigated. Two private-key systems are based on two predetermined randomly constructed sparse matrices and rely on exploiting physical properties of the Mackay-Neal (MN) low-density parity-check (LDPC) error-correcting codes are proposed. One is error correcting private-key system, which is powerful to combat ciphertext errors in communications and computer systems. The other is a private-key system with authentication.

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

The dynamic response and stochastic resonance of a kinetic Ising spin system （ISS） subject to the joint action of an external field of weak sinusoidal modulation and stochastic white-nolse are studied by solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows that the characteristic stochastic resonance as well as nonequilibrium dynamic phase transition （NDPT） occurs when the frequency ω and amplitude h0 of driving field, the temperature t of the system and noise intensity D are all specifically in accordance with each other in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to a zero- and a unit-dynamic order parameter. The NDPT boundary surface of the system which separates the dynamic paramagnetic phase from the dynamic ferromagnetic phase in the 3D parameter space of ho-t-D is also investigated. An interesting dynamical ferromagnetic phase with an intermediate order parameter of 0.66 is revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. The intermediate order dynamical ferromagnetic phase is dynamically metastable in nature and owns a peculiar characteristic in its stability as well as the response to external driving field as compared with a fully order dynamic ferromagnetic phase.

Mean-Field Studies of a Mixed Spin-3/2 and Spin-2 and a Mixed Spin-3/2 and Spin-5/2 Ising System with Different Anisotropies

The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromag- netic system with different anisotropies are studied by means of mean-field theory （MFT）. The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and trieritical line.

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.

Ferroelectricity in a diatomic Ising chain as investigated by the elastic Ising model

An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca3CoMnO6, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca3Co2-xMnxO6 （x ≈ 0.96） （Phys. Rev. Lett. 100 047601 （2008））, although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.

Magnetic properties of bilayer nano-stanenelike structure with Ruderman-Kittel-Kasuya-Yoshida coupling

A bilayer nano-stanene-like structure with Ruderman-Kittel-Kasuya-Yoshida(RKKY)coupling described by the Ising model is proposed. The magnetic and thermodynamic properties are studied using the effective-field theory with correlations. The exchange coupling,longitudinal magnetic field, number of non-magnetic layers, and anisotropies had major influences on the magnetization, specific heat, and internal energy. Different saturation magnetizations are observed on the magnetization curve. The variation in the system blocking temperature is studied. The results provide theoretical guidance for the magnetic investigation of nanomaterials with RKKY coupling.