The influence of fixed spins on the thermodynamic behavior of an Ising ferromagnet

We study the thermodynamic behavior of a ferromagnetic Ising system on a Bethe lattice in the presence of given boundary conditions. More specifically, we study the interface of the system when the spins on half of the surface are fixed opposite to the spins on the other half. We find an interface width that remains finite in the whole range (0,T _c ), a feature due to the special topology of the Bethe lattice. We also study the case where the spin on a certain lattice site belonging to a domain is fixed in a direction opposite to the domain magnetization at all temperaturesT _c . We obtain the influence of that spin on the local magnetization, and we find that the fixed spin nucleates a local domain that extends over a distance of only a few lattice sites from it at all temperaturesT _c .     

Field-induced particle pairing in an Ising system

We study the thermodynamic behavior of an Ising system on a Bethe lattice in which rearranging particles are decorating with their presence the bonds of the system, causing the local exchange coupling to depend on the decoration status. Such magnetic models have been proposed in efforts to understand the mechanisms responsible for the pairing of electrons in high-T_c superconductivity. In order to study in some detail this aspect, we focus on the question of conditions under which particle pairing occurs, and more specifically, on the role of an external magnetic field. We find a low-temperature region of the phase diagram where significant particle clustering occurs when the field is introduced.     

Block spins in the edge of an Ising ferromagnetic half-plane

The characteristic function of a block spin in the face of an Ising ferromagnetic half-plane is obtained in closed form. The distribution function for the block spin converges to a Gaussian at the critical temperature, but the normalization of the block is modified.Partially supported by NRC grant A9344.     

Thermodynamics of a model wih interacting annealed bond impurities on the Bethe lattice

A magnetic model is considered consisting of annealed, mutually repelling ferromagnetic bond impurities in an antiferromagnetic host lattice. Using recurrence relation techniques, the grand-canonical version of this model is solved on the three-coordinated Bethe lattice. A generic phase diagram is obtained containing, apart from the usual ferro- and antiferromagnetic regimes, two distinct incommensurate phases as well as a period-four modulated phase. Evidence is obtained that in one of the two incommensurate phases impurity pairing occurs.     

Loop effects in the Ising spin glass on the Bethe-like lattices

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.     

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at T_c= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β / υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.     

Interface sharpness in the Ising system

A simple proof is given for the existence of a sharp interface in three-dimensional Ising systems, at least up to the critical temperature of the corresponding two-dimensional system.     

Zero-temperature dynamics for the ferromagnetic Ising model on random graphs

We consider Glauber dynamics at zero temperature for the ferromagnetic Ising model on the usual random graph model on N vertices, with on average γ edges incident to each vertex, in the limit as N→∞. Based on numerical simulations, Svenson (Phys. Rev. E 64 (2001) 036122) reported that the dynamics fails to reach a global energy minimum for a range of values of γ. The present paper provides a mathematically rigorous proof that this failure to find the global minimum in fact happens for all γ>0. A lower bound on the residual energy is also given.     

Exact thermodynamic behavior of a generalized spin-isospin ising system on the Bethe lattice

We study a generalized Ising system consisting of a Bethe lattice on every site of which two spin-1/2 and two isospin-1/2 (or atomic species A) states can be realized, the spin-species interacting with appropriate nearest neighbor couplings. The system is equivalent to that of four states per site and we obtain its exact thermodynamic behavior. The case of a fixed concentration of species is the annealed or liquid magnetic binary alloy. The temperature dependence of the short-range-order (SRO) parameter of such systems is obtained as an application of the theory and discussed in connection with relevant material from the literature. When fixing both the concentration and the nearest neighbor spatial correlation of the species, we obtain Eggarter's formulas for the frozen-in species problem, which therefore are only approximately valid even on the Bethe lattice.     

Response factorization of simply connected Ising lattices with application to bethe lattice spin glasses

The thermodynamics of a classical lattice gas in Ising form, with arbitrary interaction, is set up in entropy format, with multipoint magnetizations as control parameters. It is specialized to the case of one- and two-point interactions on a simply connected lattice; both entropy and profile equations are written down explicitly. Linear response functions are expressed in Wertheim-Baxter factorization and used to derive the Jacobian of the transformation from couplings to magnetizations. An arbitrary spin-glass coupling distribution is transformed to the corresponding magnetization distribution, whose effect on thermodynamic properties is assessed. A Gaussian coupling-fluctuation expansion diverges at sufficiently large fluctuation amplitude, suggesting the possibility of a phase transition.     

Results from the Holsztynski-Slawny reduction method for ferromagnetic Ising models

We establish a variety of results using the Holsztynski-Slawny reduction method to study various ferromagnetic, Ising spin systems. The results range from a new proof of the lack of a first-order phase transition for certain infinite range, pair interaction, one-dimensional systems to a study of certain three-dimensional systems having many-body interactions.     

Domain growth in the three-dimensional dilute Ising model

We investigate the kinetics of domain growth in the three-dimensional Ising model with quenched random site dilution, using Monte Carlo simulation technique. A crossover from the power law growth regime to a much slower growth observed in our simulation is interpreted through the roughening of the interfaces by the quenched impurities. The results are also compared with the corresponding results in two dimensions.     

A three dimensional ferromagnetic Ising ‘fluid’ model

The three dimensional ferromagnetic spin-half Ising model with an arbitrary external magnetic field is considered in the spatial continuum limit and under a certain tempering condition to be imposed on the pair-wise spin-spin interaction. An expression for the partition function has been obtained for a tempered RKKY type interaction. The solution predicts the classical mean-field behaviour above a critical temperature below which the spontaneous magnetization jumps discontinuously from zero to the saturation value.     

Reentrant phase transitions and multicompensation points in the mixed-spin Ising ferrimagnet on a decorated Bethe lattice

A mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration–iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.     

On the ferromagnetic Ising model in noninteger spatial dimension

Using the necessary and sufficient conditions in terms of the high-field series coefficients that the Yang-Lee theorem holds, we prove rigorously by counterexample that it cannot be extended to general noninteger dimension, when such models are defined by the natural analytic continuation.Work supported in part by the US DOE.     

界面各向异性对双层铁磁薄膜自旋波性质的影响

在海森堡模型的基础上,采用界面参数化方法,将双层铁磁薄膜中自旋波本征值问题归结为联立求解能量约束方程和界面参数化方程.重点研究了界面各向异性对薄膜中自旋波本征问题的影响.结果表明:界面各向异性使对称模的波形在界面处呈现明显的钉扎现象,且界面模的能量随各向异性场增强而增大.     

Interface sharpness in the Ising model with long-range interaction

For the 3-dimensional Ising model with long-range interaction, Gibbs states are constructed that are small perturbations of non-translation-invariant ground states. These ground states are in one-to-one correspondence with the set of all rational planes.     

Bethe-Peierls approximation for the disordered Ising model

We study the Ising model for an alloy with an arbitrary number of components. We develop an approximation which reduces to that of Bethe and Peierls when the concentration of one of the components is unity. We investigate within this approximation the dependence of the various thermodynamic quantities, in particularT _c, on the composition of the alloy and the magnetic properties of its constituents. Comparison with the only exact calculation available, that of F. T. Leeet al., for a linear chain, shows extremely satisfactory agreement.Research supported by ARO (D). It has also benefited from the general support of Materials Science at the University of Chicago by the NSF.     

The interface of the Ising model and the Brownian sheet

We study the limit theorem related to the interface of the three-dimensional Ising model. Dobrushin proved that the interface does not fluctuate and becomes rigid for sufficiently large. We define the random fieldX ^L (t, s), 0t, s1, on the interface, and prove that X^L(t, s) converges to the Brownian sheet as L for sufficiently large, whereL denotes the size of the system. This result does not mean that the interface itself converges to the Brownian sheet.