Griffiths' singularities in diluted ising models on the Cayley tree
- 44 Downloads
The Griffiths singularities are fully exhibited for a class of diluted ferromagnetic Ising models defined on the Cayley tree (Bethe lattice). For the deterministic model the Lee-Yang circle theorem is explicitly proven for the magnetization at the origin and it is shown that, in the thermodynamic limit, the Lee-Yang singularities become dense in the entire unit circle for the whole ferromagnetic phase. Smoothness (infinite differentiability) of the quenched magnetizationm at the origin with respect to the external magnetic field is also proven for convenient choices of temperature and disorder. From our analysis we also conclude that the existence of metastable states is impossible for the random models under consideration.
Key WordsLee-Yang singularities Griffiths' singularities infinite differentiability metastable states
Unable to display preview. Download preview PDF.
- [Fi] M. E. Fisher, “The Theory of Condensation and the Critical Point,”Physics 3:255–283 (1967).Google Scholar
- [F] J. Fröhlich, “Mathematical Aspects of the Physics of Disordered Systems,” inCritical Phenomena, Random System and Gauge Theories, K. Osterwalder and R. Stora, eds. (Elsevier, Amsterdam, 1986).Google Scholar
- [MW] B. McCoy and T. T. Wu, “The Two Dimensional Ising Model” (Cambridge, Harvard University Press, 1973).Google Scholar
- [Mo] J. L. Monroe, “Comment on “Fractal Dimension of the Julia Set Associated with the Yang-Lee Zeros of the Ising Model on the Cayley Tree,” F. A. Boscoet al.,”Europhysics Letters 29:187–188 (1995).Google Scholar
- [T] E. C. Titchmarsh, “The Theory of Functions” (Oxford University Press, Second Edition, 1939).Google Scholar