Non-existence of spontaneous magnetization in a one-dimensional Ising ferromagnet

It is proved that an infinite linear chain of spins μ _j =±1, with an interaction energy $$H = - \Sigma J(i - j)\mu _i \mu _j $$ has zero spontaneous magnetization at all finite temperatures, provided thatJ (n) is non-negative and that $$H = - \Sigma J(i - j)\mu _i \mu _j $$ . This shows that a theorem ofRuelle, establishing the absence of long-range order when the sum Σn J (n) converges, is not the best possible.     

Dynamic behavior of a uniaxial ferromagnet near a magnetic phase-transition point

It is shown in this paper that in the sense of the dynamic behavior a uniaxial ferromagnet magnetized along the difficult direction is equivalent near a magnetic phase-transition point to some nonlinear oscillator, described by the Duffing differential equation. The frequency dependence of absorption and dispersion signals is studied and the existence of a crunode point of the dispersion curve is shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 65–68, July, 1978.In conclusion, the author is grateful to M. I. Kurkin for supervising the research and discussing its results.     

Magnetic properties of a diluted spin- Ising ferromagnet

Magnetic properties (magnetization curve, magnetization process, specific heat and paramagnetic susceptibility) of a diluted spin- Ising ferromagnet on a honeycomb lattice are examined by the use of the new formulation based on both the Ising spin identities and the differential operator technique. We find a number of characteristic phenomena, for the system with a negative value of the crystal-field constant in the special region. The physical background is also discussed.     

Ising ferromagnet with biquadratic exchange

A spin one Ising system with biquadratic exchange, is investigated, using Green's function technique in random phase approximation (RPA). Transition temperature T_c and <(S^z)²> at T_c, are found to increase with biquadratic exchange parameter α for sc, bcc and fcc lattices. The variation of <(S^z)²> at T_c with α is found to be the same for the above lattices.     

Transition temperature of an Ising ferromagnet

By calculating the partition function over all one-break configurations the transition temperature of a one-dimensional Ising ferromagnet, with inverse-square interaction, is determined.     

Susceptibility of the rectangular Ising ferromagnet

The critical index values= 7/4 for the susceptibility and=15 for the critical isotherm are derived rigorously for the rectangular Ising ferromagnet with nearest neighbor interactions. The critical indices associated with the Fisher moment definition of the correlation length are obtained asTT _c+. The index of the fluctuation sum definition of critical correlations is obtained.Partially supported by grant PHY 76 17191.     

Collapse of transient nucleation fluxes in a cold Ising ferromagnet

We report the time-dependent nucleation fluxes and associated nucleation rates in a metastable Ising ferromagnet on square lattice with Metropolis (Glauber-type) dynamics. It is discovered that, with lowering of the temperature, fluxes collapse into several representative transient curves corresponding to magic cluster sizes. Those can be associated with physical droplets, i.e., long-lived configurations which provide a link with the classical Becker-D?ring picture.     

Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field.     

Biquadratic exchange in the diluted Ising ferromagnet

Effects of biquadratic exchange on Curie temperature and specific heat have been studied in the light of a new effective field theory for the Ising Spin System. The nearest neighbour interaction is taken into account.     

Ising model of a dilute ferromagnet in the self-consistent field approximation

The method of averaging over the exchange interaction fields has been considered as applied to clusters of one and two magnetic atoms in the Ising model of a dilute ferromagnet, and a variant of fixed-scale group renormalization on the basis of this method has been constructed. It has been shown that the approximation obtained makes it possible to distinguish models with the site and bond dilutions.     

Localized magnetic excitations of coupled impurities in a transverse Ising ferromagnet

A Green's function formalism is used to calculate the spectrum of excitations of two neighboring impurities implanted in a semi-infinite ferromagnetic. The equations of motion for the Green's functions are determined in the framework of the Ising model in a transverse field and results are given for the effect of the exchange coupling, position and orientation of the impurities on the spectra of localized spin wave modes.     

Metastability in a long range one-dimensional Ising model

Decay of the metastable state of the one-dimensional Ising model with an x^-α potential is investigated using instanton (critical droplet) techniques. Calculations indicating that the analytic structure of the free energy is modified by droplet-droplet interactions for 1 < α ? 1.2 are presented.     

Critical behavior in the amorphous Ising ferromagnet with a random field

Within the differential operator method and the effective-field approximation, the critical behaviour of the amorphous Ising ferromagnet with a random field is studied. Tricritical points and reentrant phenomena are discussed. The influence of the random field and the amorphization on the transition temperature is also investigated.     

n-point functions for the rectangular Ising ferromagnet

A new representation for then-point functions of the Planar Ising ferromagnet is given. Below the critical temperature the boundary conditions are toroidal; the state is a superposition of the extremal invariant ones, with equal weights.Supported by the Fonds National Suisse de la Recherche Scientifique, by the National Science Foundation Grant No. PHY 76-17191, and by the National Research Council of Canada Grant No. NRC A 9344     

Studies of high-field magnetization in the amorphization of a crystalline Ising ferromagnet

The high-field magnetization for the amorphization of a Ising ferromagnet in a square lattice is investigated. The exchange parameters are assumed to have a delta function distribution. From the examination of the approach of magnetization to saturation, some informations about the structural inhomogeneities in the amorphization are obtained.     

Spin-one Ising ferromagnet with three-site four-spin interaction

For the Ising ferromagnet with S = 1 the effects of the three-site four-spin interaction J′ on the magnetization and the Curie temperature have been calculated using the three-spin model approximation and its effect is shown to be significant for negative value of J′.