H. H. Chen

Low-temperature behavior of a one-dimensional random Ising model

The random Ising chain is a very simple model with a large number of metastable states. Simple analytical calculation of the relaxation of energy and magnetization is presented. The effect of a nonzero magnetic field is discussed qualitatively. The slow relaxation in this simple model resembles that observed in spin glasses. A weak magnetic field can produce rather strong effects. The magnetization is shown to be a nonanalytic function of the field. The field also greatly alters the metastability characteristics.

Planar classical Heisenberg model with biquadratic interactions

Seven coefficients in the high temperature series expansions for the zero-field susceptibility and the specific heat are derived for the planar classical Heisenberg model with biquadratic interactions. The critical temperatures and the susceptibility exponents are determined for cubic lattices.

High Temperature Series Expansions for a Spin‐One Model of Ferromagnetism

We have derived the first five terms of the high temperature series expansions of the dipole and quadrupole susceptibilities for an arbitrary lattice with pair interactions described by an isotropic spin one Hamiltonian H=−JΣ〈ij〉{Si·Sj+α(Si·Sj)2}. The dipole and quadrupole phase transition temperatures are determined from these series for a face centered cubic lattice for J>0 and for −0.5≤α≤2. These temperatures correspond to the stability limit of the high temperature phase. A first order transition can occur at a higher temperature. For α=0 and 1 the transition temperatures agree with those found for the Heisenberg and exchange models. From the high temperature series we predict transition temperatures kT/J which are always lower than those found in the molecular field and constant coupling approximations for 0≤α≤1. For α>1 the molecular field approximation predicts only quadrupole ordering. By using high temperature series we have not been able to ascertain whether there is any ordering of the dipoles ...

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.

Cooperative Jahn‐Teller Effect in Dysprosium Antimonide

We have analyzed the recent magneto‐thermal and elastic data on dysprosium antimonide. Within the framework of the molecular field approximation we fit the data by using a model Hamiltonian which contains besides the crystal field term, bilinear and biquadratic pair interactions and a strain coupling of the lattice to the magnetic ions. The softening of the elastic constant (1/2)(C11‐C12) above the transition at 9.5°K is due to a strain coupling. This coupling dominates over the remaining biquadratic pair interactions of comparable magnitudes but opposite signs. We determine the bilinear coupling by fitting the magneto‐thermal data below the ordering temperature. We find that in DySb the biquadratic coupling is as important as the bilinear.

Cluster variation studies of the anisotropic exchange interaction model

The cluster variation method is applied to study critical properties of the Potts-like ferromagnetic anisotropic exchange interaction model. Phase transition temperatures, order parameter discontinuities and latent heats of the model on the triangular and the fcc lattices are determined by the triangle approximation; and those on the square and the sc lattices are determined by the square approximation.

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.

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.

Quadrupole phase transition of a planar classical Heisenberg model

The quadrupole phase transition of a planar classical Heisenberg model with biquadratic interactions is investigated by the high-temperature series expansion method. From the quadrupole susceptibility series the critical temperatures and the critical exponents are determined for cubic lattices.