Interface free energy for two dimensional Ising models

The interface free energy of an Ising model with nearest neighbour interactions on a generalized square lattice is calculated using a simple method suggested by Müller-Hartmann and Zittartz. For certain values of the coupling constants this lattice can be made to be topologically equivalent to either a hexagonal or triangular lattice. The method of calculation bypasses the full bulk problem by considering only special interface configurations of the spins. It is shown that a large number of exactly known results for these different types of lattice can be obtained using this simple method.     

Interface properties of the three-state potts model in two dimensions

Interface properties, in particular the interface free energy and the interface profile of the three-state Potts model in two dimensions are studied using Monte Carlo techniques and a generalized version of the method of Müller-Hartmann and Zittartz. The role of the third state in characterizing the interface between the two other states is elucidated.     

Phase diagram of the antiferromagnetic triangular Ising model with anisotropic interactions

It is argued that there exist two antiferromagnetic phases in the triangular Ising model with anisotropic interactions. A method due to Müller-Hartmann and Zittartz (MZ) is used to derive a closed-form expression for the phase boundary. We also give a criterion under which the MZ method is expected to be applicable and accurate.Work supported in part by a grant from the National Science Foundation.     

Lifshitz points in ising systems

Phase diagrams of Ising systems with competing interactions are calculated using (a) the method of Müller-Hartmann and Zittartz to determine the transition temperature via the vanishing of an interface free energy (b) a Migdal-Kadanoff bond-moving scheme and (c) Monte Carlo simulations. It is shown that in two-dimensional Ising systems a uniaxial Lifshitz point can exist at non-zero temperatures, whereas the lower critical dimensiond _l for a Lifshitz point in a system with identical competing interactions along each of its cartesian axis isd _l 2.     

Second-order phase transitions in triangular ising models with two- and three-spin interactions

For Ising models with pair and three-spin interactions on the triangular lattice the nature of the phase diagram in the temperature-field plane is studied. Second-order transitions are located by the interface method of Müller-Hartmann and Zittartz.     

Phase boundary of the square-lattice Ising antiferromagnet by real space renormalization group methods

The transition temperature of the square lattice Ising antiferromagnet at finite magnetic field is calculated by three different approximations within the real space renormalization group approach. The most refined approximation is an extension of Kadanoff's potential moving method to a larger cell-size. The results of this approximation are in good agreement with recent Monte Carlo simulations and the Müller-Hartmann/Zittartz conjecture for the phase boundary.     

Continuous order phase transitions on a decorated Cayley tree of connectivity two

The treatment of the Ising model on a Cayley tree given by Müller-Hartmann and Zittartz is extended in the case of connectivity two to a decorated tree containing additional bonds with an arbitrary coupling constant. The possibility of phase transitions is investigated and discussed. The positions of the singular surfaces, on which continuous order phase transitions take place, are examined as functions of coupling constants and external fields.     

Nuclear orientation experiemnts on Al2LaCe alloys

Nuclear orientation experiments on ^137mCe impurities in Al₂La show directly at almost 0 K that these alloys correspond to the magnetic conditions assumed by Müller-Hartmann and Zittartz.     

Kondo impurities in anisotropic superconductors. Eliashberg formulation

The Kondo effect in an anisotropic superconductor is studied within the framework of the Migdal-Eliashberg (ME) formulation of superconductivity. The renormalization of the ME equations arising from the scattering by the Kondo impurities is obtained on the basis of the Müller-Hartmann and Zittartz theory. Both the decrease of the transition temperature T_c and the specific heat jump at T_c are calculated.     

Higher-order susceptibilities of the regular and the random Ising model on the Cayley tree. I

Explicit expressions for the fourth-order susceptibility (⁴), the fourth derivative of thebulk free energy with respect to the external field, are given for the regular and the random-bond Ising model on the Cayley tree in the thermodynamic limit, at zero external field. The fourth-order susceptibility for the regular system diverges at temperature T _c ⁽⁴⁾ = 2k _B ^–1 J/ln{1+2/[(z–1)^3/4–1]}, confirming a result obtained by Müller-Hartmann and Zittartz [Phys. Rev. Lett. 33:893 (1974)]; Herez is the coordination number of the lattice,J is the exchange integral, andk _B is the Boltzmann constant. The temperatures at which ⁽⁴⁾ and the ordinary susceptibility (²) diverge are given also for the random-bond and the random-site Ising model and for diluted Ising models.     

Magnetic impurity effects inAgMn,AuFe, andCuCr studied by tunneling in superconducting proximity layers

Magnetic interactions were studied by superconducting tunneling into diluteAgMn,AuFe, andCuCr alloys in which superconductivity had been induced by a proximity effect. A detailed investigation ofAgMn, for concentrations up to 0.4 at.% Mn and at temperatures down to 0.05 K, revealed a weak impurity band within the energy gap of the density of excited states at about 0.68 of the half energy gap . The amplitude of the band, however, was twenty times smaller than expected from the theory by Müller-Hartmann and Zittartz. This makes the interpretation of the effect as being due to bulkAgMn doubtful. The localisation of the band would imply a Kondo temperature,T _K , of about 1 mK for an impurity spinS=5/2. No effect of spin-glass ordering was seen in the temperature dependence of the tunneling density of states inAgMn which contradicts a report by Schuller et al. The zero bias conductance could instead be reproduced from low temperature measurements if the temperature variation in was taken into account. InCuCr, the shape of the impurity band was found to be temperature dependent. The location of an impurity band at about 0.68 inAuFe indicates. together with previous observations, the presence of two impurity bands in this alloy. The one found here, might be due to long-range Fe pairs.     

The S-J exchange interaction under the influence of the crystalline field

A magnetic impurity, having the s-j interaction with conduction electrons, under the crystalline field of host metals is investigated. The Hamann integral equation for the t-matrix can be derived and solved by the method of Zittartz and Müller-Hartmann for the cases of (1) small splittings, yielding the Kondo anomaly and decrease of the Kondo temperatureT _K compared with no splittings, (2) a large splitting from the crystalline ground doublet state, producing the higherT _K by the exicited level, and (3) a large splitting from the ground singlet state giving no Kondo effect. The macroscopic properties are calculated for (1) and (2).     

The local pressure for one dimensional sticky rods

Thermodynamic properties of inhomogeneous one dimensional classical systems with nearest neighbor interactions are considered. In particular the partition function of a system of hard core particles with a zero range attractive interaction is determined in the presence of an arbitrary external potential. Different concepts of a local pressure are developed and compared with each other.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Analyticity of the free energy of the two-dimensional random Ising model

It is shown that the systematic-expansion method of the free energy of the two-dimensional random Ising model, by Hoever and Zittartz, does not lead to evidence for the absence of a spin glass transition as they claimed.     

The specific heat jump of superconducting La1-xTbxAl2 related to crystal electric field splitting of the Tb3+ levels

Measurements of the specific heat jump Δc(Tinc) were performed on superconducting La_1-xTb_xAl₂ compounds in order to investigate the pairbreaking effect of Tb³⁺ ions in the LaAl₂ host. The results deviate from the Abrikosov-Gorkov theory for superconductors with magnetic impurities. Taking into account the crystal field level structure of Tb³⁺ in LaAl₂ the results can be qualitatively understood within the model of Fulde, Keller and Peschel. According to calculations published by Müller-Hartmann and Zittartz an influence of the Kondo effect can be ruled out.     

Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.     

Hard-square lattice gas

We have studied the hard-square lattice gas, using corner transfer matrices. In particular, we have obtained the first 24 terms of the high-density series for the order parameter ₂– ₁. From these we estimate the critical activity to be 3.7962±0.0001. This is in excellent agreement with the earlier work of Gaunt and Fisher. It conflicts with the value 4.0 given by Müller-Hartmann and Zittartz's formula for the critical point of the antiferromagnetic Ising model in a field, so we conclude that this formula, while a good approximation, is not exact.     

Interface free energy and transition temperature of the square-lattice Ising antiferromagnet at finite magnetic field

We use a simple method to calculate interface properties of the square-lattice Ising antiferromagnet with nearest neighbour interaction. The method bypasses the more complicated bulk problem by taking into account only interface configurations of spins and allows the inclusion of a finite magnetic field. From this we derive two new results: 1) the interface free energy associated with the coexistence of the two antiferromagnetic phases at finite magnetic field, and 2) the transition temperature as a function of the magnetic field which determines the phase boundary.     

Spin compensation temperatures induced by longitudinal fields in a mixed spin-3/2 and spin-5/2 Ising ferrimagnet

I studied the ferrimagnetic Ising model with nearest neighbour interactions for a square lattice and simple cubic one, using mean field theory. The free energy of a mixed spin Ising ferrimagnetic model was calculated from a mean field approximation of the Hamiltonian. By minimizing the free energy, I obtained the equilibrium magnetizations and the compensation temperatures. Clear indications of the single-ion anisotropies on the compensation points of the mixed spin-3/2 and spin-5/2 ferrimagnetic lattices are found. Some interesting behaviors of these systems are obtained depending not only on the values of magnetic anisotropies for both sublattice sites but also on the lattice structure. The longitudinal magnetic fields dependence of the spin compensation temperature is the main focus of research. The possibility of many compensation temperatures is indicated.     

Spin- and charge density perturbations and short-range order in Fe–Cu and Fe–Zn BCC alloys: A Mössbauer study

A model used to describe the ⁵⁷Fe Mössbauer spectra for the binary BCC iron alloys rich in iron has been extended to account for the alloy crystallographic ordering. The ordering is accounted for by introducing single order parameter. Extension of the model is described in detail. The model has been tested applying it to the Fe–Cu alloys obtained by the arc melting and to the Fe–Zn alloys prepared by the solid state reaction. Random alloys are obtained up to ∼2 at% of Cu, and up to ∼8 at% of Zn. For higher impurity (minor alloy component) concentration it has been found that Cu atoms try to avoid Fe atoms in the iron matrix as nearest neighbors, while the opposite happens to the Zn atoms, albeit at much lesser scale, i.e., Zn–Zn interactions are much weaker than Fe–Zn interactions at the nearest neighbor distance. Perturbations to the iron magnetic hyperfine field (spin density) and electron (charge) density on the iron nucleus have been obtained for both series of alloys versus impurity concentration.