Felix Lee

Interface effects on the critical temperature of heterostructures of magnetic films

The analytical approach to the critical point of Ising films proposed recently by Lin et al is extended to investigate the interface effects on the critical temperature for magnetic bilayer heterostructures. We consider heterostructures composed of an m-monolayer film grown on a substrate of an n-monolayer magnetic film with different lattice structures where and . The mean of the bilayered heterostructure as a whole is obtained as a function of the total thickness N = m + n of the inhomogeneous system. A strong dependence of the critical temperature upon the lattice structure is revealed. In particular, interface effects on for systems consisting of an overlayer of a few spin monolayers on a thin film of magnetic substrates with different lattice structure are investigated in detail and results for various combinations of the lattice structure are discussed.

Quantum Monte Carlo study of the one-dimensional exchange interaction model

Abstract Handscombs quantum Monte Carlo method is applied to calculate the zero-field susceptibility of the one-dimensional spin- S exchange interaction model. Analyses of these data show that the exponents γ = 2 and ν = 1 for all spin values.

Migdal-Kadanoff renormalization for the exchange interaction model

Abstract The Migdal-Kadanoff (MK) renormalization group transformation is derived for the spin-S exchange interaction model. Both the standard MK approach and a modified MK method are used to determine critical temperatures of the model for various spin values.

General‐temperature series expansion for Ising systems

A linked‐cluster expansion technique for spin systems has been used to obtain the free energy, the magnetization, and the susceptibility series for three Ising systems: (1) The Ising model; (2) The Blume‐Capel model; and (3) The Blume‐Emery‐Griffiths (BEG) model. Each Hamiltonian is first divided into a single‐ion potential and a term describing the interaction of the spin fluctuations. Only the latter is treated as perturbation in the series expansion. In the parametric phase our series reduces to the exact high‐temperature series. However, in the ordered phase the same series can be used to study the low temperature behavior, such as the variation of the magnetization with temperature. The analysis of the eighth‐order series for systems (1) and (2) show results in excellent agreement with the previous ones obtained from the high‐temperature and low‐temperature series. The series analysis for the BEG model shows quite different behavior from that predicted by the mean‐field approximation.

Low-temperature series expansions for lattices of non-integral dimensions☆

Abstract Low-temperature series expansions for Ising models on lattices of non-integral dimensions are studied. Critical exponents β for various dimensions are extrapolated from series expansions for the generalized equivalent neighbor lattice.

Numerical representation and identification of graphs

A method to represent each linear graph by a single number, the determinant of its modified incidence matrix, is introduced. The isomorphism of graphs can be determined by comparing the determinants of their incidence matrices. Although it is not proved that different graphs can always be distinguished by the determinants of their modified incidence matrices, the proposed method provides a good practical algorithm for the identification of graphs. Applications of the single‐number representation of graphs are discussed.

Lattice constant systems and some of their properties

Lattice constants are defined in a general way such that weak lattice constants, strong lattice constants, free multiplicities and coincidable occurrence factors are cases of the generalised lattice constants. A general method to express a lattice constant of one system as a linear combination of lattice constants of another system is described. Some properties of the conversion matrices are discussed. A systematic method to express the lattice constant of a reducible graph in terms of lattice constants of irreducible graphs is also studied.

An equivalent neighbor model for a lattice of arbitrary dimensionality, having any anisotropy and range of interaction

Abstract High-temperature series expansions are derived for a lattice model in which the lattice dimensionality, the range of interaction and the degree of lattice anisotropy are continuous variables. Critical properties of the Ising model on the present lattice are reported.

Linked cluster series expansion and phase transitions in complex models

We show that the use of the linked‐cluster series expansion aided by the extrapolation techniques is an effective method in the study of complex models which display first‐order phase transitions as well as second‐order phase transitions. The Blume–Capel model is used for the demonstration.

Zero temperature series expansion for an easy-plane spin-one ferromagnet

Abstract The first six coefficients in the susceptibility series have been obtained for an easy-plane spin-one ferromagnet at zero temperature. The results are for a general lattice and for arbitrary range of interaction. We, however, present only the series for the fcc and the triangular lattices. Estimates of the critical points and the critical exponents are given.