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Central University of Tamil Nadu 
M Ponmurugan 
Corresponding Authors:
M Ponmurugan, S V M Satyanarayana 
DOI #: 
The Θ points of interacting self-avoiding walks and rings on a 2D square lattice 
Journal of Statistical Mechanics: Theory and Experiment 
classical Monte Carlo simulations, finite-size scaling, phase transformations 
We propose an order parameter to locate the Θ points of interacting self-avoiding walks (ISAWs) and self-avoiding rings (SARs) on a two dimensional square lattice. Using exact enumeration results for ISAWs of finite size we find that the order parameter as a function of temperature shows a discontinuous jump at the transition temperature. The computed transition temperature fluctuates with the size of the walk and appears to converge well to the Θ point as the size increases. The value for the Θ point of the linear homopolymer phase transition obtained from our method agrees with recent high precision Monte Carlo estimates. We tested the reliability of our method for longer walk lengths by using the density of states obtained from the recently proposed flat energy histogram method. The Θ point is also computed for SARs on a square lattice using exact enumeration results available in the literature. Using two other independent methods, namely the partition function zeros on the complex temperature plane and the inflection point of microcanonical entropy, the Θ point of an SAR is computed and is found to be in agreement with the result obtained with the proposed order parameter. 
Entered by:
M Ponmurugan on 2020-09-06 
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