EPJ Web of Conferences
Volume 108, 2016Mathematical Modeling and Computational Physics (MMCP 2015)
|Number of page(s)||12|
|Section||Plenary and Invited Lectures|
|Published online||09 February 2016|
Exact Partition Functions of Interacting Self-Avoiding Walks on Lattices
1 Department of Physics, National Taiwan University, Taipei 106, Taiwan
2 Institute of Physics of Academia Sinica, Nankang, Taipei 11529, Taiwan
3 Department of Physics, National Dong-Hua University, Hualien 974, Taiwan
4 National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu 30013, Taiwan
5 Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
Published online: 9 February 2016
Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW) on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping Cυ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.
© Owned by the authors, published by EDP Sciences, 2016
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.