Puiseux Series Expansions for the Eigenvalues of Transfer Matrices and Partition Functions from the Newton Polygon Method for Nanotubes and Ribbons
Jeffrey R Schmidt* and Dileep Karanth
Department of Physics, University of Wisconsin-Parkside, USA
- *Corresponding Author:
- Dr. Jeffrey R Schmidt
Mathematics and Physics
University of Wisconsin-Parkside
900 Wood Road, Kenosha, Wisconsin 53141, USA
E-mail: [email protected]
Received Date: July 27, 2013; Accepted Date: February 28, 2014; Published Date: March 10, 2014
Citation: Schmidt JR, Karanth D (2014) Puiseux Series Expansions for the Eigenvalues of Transfer Matrices and Partition Functions from the Newton Polygon Method for Nanotubes and Ribbons. J Phys Math 5:125 doi: 10.4172/2090-0902.1000125
Copyright: © 2014 Schmidt JR, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
For certain classes of lattice models of nanosystems the eigenvalues of the row-to-row transfer matrix and the components of the corner transfer matrix truncations are algebraic functions of the fugacity and of Boltzmann weights. Such functions can be expanded in Puiseux series using techniques from algebraic geometry. Each successive term in the expansions in powers a Boltzmann weight is obtained exactly without modifying previous terms. We are able to obtain useful analytical expressions for any thermodynamic function for these systems from the series in circumstances in which no exact solutions can be found.