摘要:

Necessary and sufficient global stability criteria are obtained which govern the stellar‐dynamic stability to axisymmetric perturbations for disk models of galaxies. They are more complicated and difficult to apply than Toomre's criterion because they are global and allow general orbits of disk equilibria. If local and epicyclic assumptions are added, they then reduce to Toomre's criterion. But unlike the latter, in these new criteria, stability is determined by some average velocity dispersion rather than its local values, thus local variations in Toomre'sQparameter appears possible

ISSN:0022-2526    

DOI:10.1002/sapm19715011

年代:1971

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm197150113

年代:1971

数据来源: WILEY

摘要:

A completely general square‐lattice ferroelectric model is considered, in which the configuration energies have arbitrary values at each vertex. It is found that the partition function can be evaluated by straightforward extensions of the method used for the regular ice, F‐ and KDP‐models, provided three sets of conditions are satisfied. These ensure that the two ordered F‐model states are degenerate (in the limit of a large lattice), so we conclude that the application of any staggered field which breaks this degeneracy also renders the problem insoluble by the present methods.The partition function for these ordered states is obtained explicitly and found to be given quite simply as a product of certain parameters associated with each vertex. Finally some conjectures are made concerning the spontaneous staggered polar

ISSN:0022-2526    

DOI:10.1002/sapm197150151

年代:1971

数据来源: WILEY

摘要:

The eigenvalue problem for the transfer matrix of the two‐dimensional Ising lattice, with free boundaries perpendicular to the transfer direction, is solved. The mathematical mechanism which produces the asymptotic degeneracy of the eigenvalue spectrum below the bulk transition temperature is different from the case with cyclic boundary conditions. The results are used to calculate the two‐spin correlation function between two spins in the same edge of the lattice, and between two spins in opposite ed

ISSN:0022-2526    

DOI:10.1002/sapm197150171

年代:1971

数据来源: WILEY

摘要:

We present a simple generalization of the Griffiths inequalities to theX ‐ Ymode

ISSN:0022-2526    

DOI:10.1002/sapm197150189

年代:1971

数据来源: WILEY