THERMODYNAMIC PROPERTIES OF FINITE CHAINS OF EXCHANGE-COUPLED ATOMS.
Abstract
The energy, entropy, specific heat, and susceptibility, all in the limit of zero external magnetic field, are computed for finite chains of spin 1/2 atoms coupled by an isotropic exchange interaction between nearest neighbors. The calculations are carried out for chains containing 2, 3, 4,....,10 atoms, and for both ferro- and antiferromagnetic coupling. The convergence as the number of atoms in the chain, N, increases suggests that the thermodynamic quantities obtained for a 9 or 10 spin chain provide a fairly good approximation to the same quantities in the limiting case of an infinite chain. At any fixed temperature the energy, Helmholtz free energy, and susceptibility as a function of N are monotone increasing (ferromagnetic case) or monotone increasing for N even and monotone decreasing for N odd (antiferromagnetic case). Similar monotone behavior is found for the antiferromagnetic entropy and specific heat (the latter only for N odd). Numerical values for energy, entropy, specific heat, and susceptibility are given for N = 9, 10. Finite chains with Ising interaction are also briefly discussed, and the thermodynamic quantities are shown to exhibit several of the monotonicity properties found for the isotropic interaction.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1961
- Accession Number
- AD0610440
Entities
People
- R. B. Griffiths
Organizations
- Stanford University