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.     

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.     

The magnetization of thin ferromagnetic film in Ising approximation (S = 12)

In the paper thin ferromagnetic films with perfect crystal structure and with structure of diluted alloy have been considered. For both cases the magnetization profiles across the film for various temperatures and various film thicknesses, together with the corresponding critical temperatures have been calculated.For the case of film with diluted alloy structure the relation of critical concentration of magnetic atoms on film thickness has been also found.     

New integral representation for the spin S Ising ferromagnet

A recently discovered integral representation for the spin $\text{1}\text{2}$ Ising ferromagnet is generalized to the case of spin S.     

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.     

Renormalization group specific heat and magnetization of the Ising ferromagnet in cubic and hypercubic lattices

A real space renormalization group approach with two-terminal clusters is proposed for the calculation of the specific heat and spontaneous magnetization (for all temperatures) of the nearest-neighbour spin –1/2 Ising ferromagnet in simple cubic and hypercubic lattices. For arbitrary temperatures only small clusters (renormalization expansion factorb=2,3 ford=3 andb=2 ford=4) are considered: they lead to reasonable values for the critical points, exponents and amplitudes, to a thermal behaviour of the spontaneous magnetization which is already quite close to what is expected (from series results for example) but to a thermal behaviour of the specific heat which is not yet very close to what is expected. The global results improve whenb increases from 2 to 3. The drastic effect (on the specific heat) of an apparently innocuous approximation is exhibited. The discussion of theT0 andT limits is performed and theexact behaviours of the free and internal energies and the specific heat are obtained for sufficiently large values ofb andall dimensionalities.On leave of absence from Laboratorio de Física Teórica. Departamento de Física, Universidad Nactional de La Plata, CC No. 67 (1900), La Plata, Argentina.     

The transverse ferromagnet spin-1 Ising model of alternating magnetic superlattice

Within the framework of the effective field theory with a probability distribution technique that accounts for the single-site spin correlations, we examine the critical behavior of the transverse ferromagnetic spin-1 Ising model of an alternating magnetic superlattice. The critical temperature of the alternating magnetic superlattice has been studied as a function of the interlayer and intralayer exchange interactions and the strength of the transverse field and the thickness of the finite superlattice. Received 12 January 2000 and Received in final form 14 September 2000     

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.     

The local magnetization of an incomplete ferromagnet

The local magnetization in the vicinity of a nonmagnetic impurity in a Heisenberg ferromagnet is calculated for different temperatures below the Curie point. In the low-temperature region the spin-wave approximation is used and calculations are carried out up to first-order perturbation theory. The deviation of the magnetization from the value in a perfect magnet turns out to be proportional to T^5/2 for very low temperatures. In the region 0.40 T_CC numerical solutions are obtained for a molecular field model, under the assumption that the influence of the impurity has a finite range. Extrapolations of both sets of results fit reasonably well together for the nearest and next nearest neighbours of the impurity.     

An Ising ferromagnet with discontinuous long-range order

An infinite one-dimensional Ising ferromagnetM with long-range interactions is constructed and proved to have the following properties. (1)M has an order-disorder phase transition at a finite temperature. (2) Any Ising ferromagnet of the same structure asM, but with interactions tending to zero with distance more rapidly than those ofM, cannot have a phase-transition. (3) The long-range-order parameter (thermal average of the spin-spin correlation at infinite distance) jumps discontinuously from zero in the disordered phase to a finite value in the ordered phase. All three properties have been conjectured by Anderson and Thouless to hold for a particular Ising ferromagnet which is relevant to the theory of the Kondo effect. AlthoughM is not identical to Anderson's model, the results proved forM support the validity of the physical arguments of Anderson and Thouless.     

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′.     

Dynamics of magnetization in ferromagnet with spin-transfer torque

We review our recent works on dynamics of magnetization in ferromagnet with spin-transfer torque. Driven by constant spin-polarized current, the spin-transfer torque counteracts both the precession driven by the effective field and the Gilbert damping term different from the common understanding. When the spin current exceeds the critical value, the conjunctive action of Gilbert damping and spin-transfer torque leads naturally the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width. Driven by space- and time-dependent spin-polarized current and magnetic field, we expatiate the formation of domain wall velocity in ferromagnetic nanowire. We discuss the properties of dynamic magnetic soliton in uniaxial anisotropic ferromagnetic nanowire driven by spin-transfer torque, and analyze the modulation instability and dark soliton on the spin wave background, which shows the characteristic breather behavior of the soliton as it propagates along the ferromagnetic nanowire. With stronger breather character, we get the novel magnetic rogue wave and clarify its formation mechanism. The generation of magnetic rogue wave mainly arises from the accumulation of energy and magnons toward to its central part. We also observe that the spin-polarized current can control the exchange rate of magnons between the envelope soliton and the background, and the critical current condition is obtained analytically. At last, we have theoretically investigated the current-excited and frequency-adjusted ferromagnetic resonance in magnetic trilayers. A particular case of the perpendicular analyzer reveals that the ferromagnetic resonance curves, including the resonant location and the resonant linewidth, can be adjusted by changing the pinned magnetization direction and the direct current. Under the control of the current and external magnetic field, several magnetic states, such as quasi-parallel and quasi-antiparallel stable states, out-of-plane precession, and bistable states can be realized. Th     

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.     

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     

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.     

Pair function for the rectangular Ising ferromagnet

A representation of the pair correlation function for the rectangular Ising model in zero magnetic field is derived using a new spinor technique; this enables the scaling limit to be established, as well as several analytical properties of the scaling functions.Supported by the Fonds National Suisse de la Recherche Scientifique, by the National Science Foundation Grant No. PHY76-17191, and by the National Research Council of Canada Grant No. NRC A9344     

Thermodynamical properties of the site-bond diluted Ising ferromagnet

Within the framework of an effective-field approximation, we calculate the magnetization, specific heat and susceptibility of a quenched site-bond diluted Ising ferromagnet in honeycomb lattice as the functions of site and bond concentrations. These results have a substantial improvement over the standard molecular field approximation.