Heat capacity decomposition by partition function zeros for interacting self-avoiding walks

¹ Department of Physics, National Dong-Hua University - Hualien 974, Taiwan
² Department of Physics, National Taiwan University - Taipei 106, Taiwan
³ Institute of Physics, Academia Sinica - Taipei 115, Taiwan

^(a) cnchen@mail.ndhu.edu.tw
^(b) huck@phys.sinica.edu.tw

Received: 10 August 2013
Accepted: 25 October 2013

Abstract

A novel method based on partition function zeros is developed to demonstrate the additional advantages by considering both loci of partition function zeros and thermodynamical functions associated with them. With this method, the first pair of complex conjugate zeros (first zeros) can be defined without ambiguity and the critical point of a small system can 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 two overlapping phase transitions can be well separated. This method is applied to the interacting self-avoiding walk (ISAW) of homopolymer with N monomers on the simple cubic lattice, which has a collapse transition at a higher temperature and a freezing transition at a low temperature. The exact partition functions Z_N with N up to 27 are calculated and our approach gives a clear scenario for the collapse and the freezing transitions.