Best-selling in Textbooks
Save on Textbooks
- AU $27.54Trending at AU $44.05
- AU $80.99Trending at AU $88.14
- AU $72.90Trending at AU $77.73
- AU $71.88Trending at AU $73.73
- AU $82.89Trending at AU $85.64
- AU $72.90Trending at AU $79.61
- AU $34.73Trending at AU $42.75
About this product
- DescriptionThe author studies a family of rermalization transformations of generalized diamond hierarchical Potts models through complex dynamical systems. He proves that the Julia set (unstable set) of a rermalization transformation, when it is treated as a complex dynamical system, is the set of complex singularities of the free energy in statistical mechanics. He gives a sufficient and necessary condition for the Julia sets to be disconnected. Furthermore, he proves that all Fatou components (components of the stable sets) of this family of rermalization transformations are Jordan domains with at most one exception which is completely invariant. In view of the problem in physics about the distribution of these complex singularities, the author proves here a new type of distribution: the set of these complex singularities in the real temperature domain could contain an interval. Finally, the author studies the boundary behavior of the first derivative and second derivative of the free energy on the Fatou component containing the infinity. He also gives an explicit value of the second order critical exponent of the free energy for almost every boundary point.
- Author BiographyJianyong Qiao, School of Science, Beijing University of Posts and Telecommunications, People's Republic of China.
- Author(s)Jianyong Qiao
- PublisherAmerican Mathematical Society
- Date of Publication30/03/2015
- Series TitleMemoirs of the American Mathematical Society
- Series Part/Volume Number234/1102
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Width178 mm
- Height254 mm
This item doesn't belong on this page.
Thanks, we'll look into this.