Skip to main content
SpringerLink
Log in

Transfer Matrix Algorithm for Computing the Geometric Quantities of a Square Lattice Polymer

  • Published:
Journal of the Korean Physical Society Aims and scope Submit manuscript

Abstract

I develop a transfer matrix algorithm for computing the geometric quantities of a square lattice polymer with nearest-neighbor interactions. The radius of gyration, the end-to-end distance, and the monomer-to-end distance were computed as functions of the temperature. The computation time scales as ≲ 1.8N with a chain length N, in contrast to the explicit enumeration where the scaling is ~ 2.7N. Various techniques for reducing memory requirements are implemented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. S. Chan and K. A. Dill, Macromolecules 22, 4559 (1989).

    Article  ADS  Google Scholar 

  2. H. S. Chan and K. A. Dill, Annu. Rev. Biophys. Biophys. Chem. 20, 447 (1991).

    Article  Google Scholar 

  3. P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1967).

    Google Scholar 

  4. P-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).

    Google Scholar 

  5. M. J. Stephen, Phys. Lett. A 53, 363 (1975).

    Article  ADS  Google Scholar 

  6. A. Baumgärtner, J. Physique 43, 1407 (1982).

    Article  Google Scholar 

  7. T. Ishinabe, J. Chem. Phys. 77, 3171 (1982); T. Ishinabe, J. Chem. Phys. 80, 1318 (1984); T. Ishinabe, J. Phys. A 18, 3181 (1985).

    Article  ADS  Google Scholar 

  8. A. L. Kholodenko and K. F. Freed, J. Phys. A 17, L191 (1984); A. L. Kholodenko and K. F. Freed, J. Chem. Phys. 80, 900 (1984).

    Article  ADS  Google Scholar 

  9. T. M. Birshtein, S. V. Buldyrev and A. M. Elyashevitch, Polymer 26, 1814 (1985).

    Article  Google Scholar 

  10. B. Derrida and H. Saleur, J. Phys. A 18, L1075 (1985).

    Article  ADS  Google Scholar 

  11. V. Privman, J. Phys. A 19, 3287 (1986).

    Article  ADS  Google Scholar 

  12. H. Saleur, J. Stat. Phys. 45, 419 (1986).

    Article  ADS  Google Scholar 

  13. B. Duplantier and H. Saleur, Phys. Rev. Lett. 59, 539 (1987).

    Article  ADS  Google Scholar 

  14. F. Seno and A. L. Stella, J. Phys. France 49, 739 (1988).

    Article  Google Scholar 

  15. P. H. Poole, A. Coniglio, N. Jan and H. E. Stanley, Phys. Rev. B 39, 495 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  16. H. Meirovitch and H. A. Lim, Phys. Rev. Lett. 62, 2640 (1989); H. Meirovitch and H. A. Lim, J. Chem. Phys. 91, 2544 (1989).

    Article  ADS  Google Scholar 

  17. I. Chang and H. Meirovitch, Phys. Rev. E 48, 3656 (1993).

    Article  ADS  Google Scholar 

  18. P. Grassberger and R. Hegger, J. Phys. I France 5, 597 (1995).

    Article  Google Scholar 

  19. G. T. Barkema, U. Bastolla and P. Grassberger, J. Stat. Phys. 90, 1311 (1998).

    Article  Google Scholar 

  20. S. L. Narasimhan, P. S. R. Krishna, K. P. N. Murthy and M. Ramanadham, Phys. Rev. E 65, 010801(R) (2001).

    Article  Google Scholar 

  21. C-N. Chen and C-Y. Lin, Physica A 350, 45 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  22. J. Zhou, Z-C. Ou-Yang and H. Zhou, J. Chem. Phys. 128, 124905 (2008).

    Article  ADS  Google Scholar 

  23. A. G. Cunha-Netto, R. Dickman and A. A. Caparica, Comput. Phys. Comm. 180, 583 (2009).

    Article  ADS  Google Scholar 

  24. M. Gaudreault and J. Viñals, Phys. Rev. E 80, 021916 (2009).

    Article  ADS  Google Scholar 

  25. S. Caracciolo, M. Gherardi, M. Papinutto and A. Pelissetto, J. Phys. A 44, 115004 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  26. M. Ponmurugan and S. V. M. Satyanarayana, J. Stat. Mech. P06010 (2012).

    Google Scholar 

  27. T. Vogel, M. Bachmann and W. Janke, Phys. Rev. E 76, 061803 (2007).

    Article  ADS  Google Scholar 

  28. T. Wüst and D. P. Landau, Phys. Rev. Lett. 102, 178101 (2009).

    Article  ADS  Google Scholar 

  29. J. H. Lee, S-Y. Kim and J. Lee, J. Chem. Phys. 133, 114106 (2010); J. H. Lee, S-Y. Kim and J. Lee, J. Chem. Phys. 135, 204102 (2011); J. H. Lee, S-Y. Kim and J. Lee, Phys. Rev. E. 86, 011802 (2012); J. H. Lee, S-Y. Kim and J. Lee, Phys. Rev. E. 87, 052601 (2013); J. H. Lee, S-Y. Kim and J. Lee, AIP Adv. 6, 055013 (2016).

    Article  ADS  Google Scholar 

  30. C-N. Chen, Y-H. Hsieh and C-K. Hu, Europhys. Lett. 104, 20005 (2013).

    Article  ADS  Google Scholar 

  31. J. H. Lee, S-Y. Kim and J. Lee, Comput. Phys. Comm. 182, 1027 (2011).

    Article  ADS  Google Scholar 

  32. Y-H. Hsieh, C-N. Chen and C-K. Hu, Comput. Phys. Comm. 209, 27 (2016).

    Article  ADS  Google Scholar 

  33. I. Jensen, arXiv:1309.6709 [math-ph] (2013).

  34. I. Jensen, J. Phys. A: Math. Gen. 37, 5503 (2004).

    Article  ADS  Google Scholar 

  35. A. R. Conway, I. G. Enting and A. J. Guttmann, J. Phys. A: Math. Gen. 26, 1519 (1993).

    Article  ADS  Google Scholar 

  36. N. Clisby and I. Jensen, J. Phys. A: Math. Theor. 45, 115202 (2012).

    Article  ADS  Google Scholar 

  37. I. Jensen and A. J. Guttmann, J. Phys. A: Math. Gen. 32, 4867 (1999).

    Article  ADS  Google Scholar 

  38. I. G. Enting, J. Phys. A: Math. Gen. 13, 3713 (1980).

    Article  ADS  Google Scholar 

  39. J. Lee, Comput. Phys. Comm. 228, 11 (2018).

    Article  ADS  Google Scholar 

  40. M. Suzuki, Phys. Rev. B 3, 2957 (1985).

    Article  ADS  Google Scholar 

  41. S-Y. Kim and R. J. Creswick, Phys. Rev. E 58, 7006 (1998).

    Article  ADS  Google Scholar 

  42. P. Bruscolini and A. Pelizzola, Phys. Rev. Lett. 88, 258101 (2002).

    Article  ADS  Google Scholar 

  43. J. Lee, Phys. Rev. Lett. 110, 248101 (2013); J. Lee, Phys. Rev. E 88, 022710 (2013).

    Article  ADS  Google Scholar 

  44. R. Bayer, Acta Informatica 1, 290 (1972).

    Article  Google Scholar 

  45. I. Jensen, J. Phys. A: Math. Gen. 36, 5731 (2003).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Bioinformatics and Life Science, Soongsil University, Seoul, 06978, Korea

    Julian Lee

Authors
  1. Julian Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Julian Lee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, J. Transfer Matrix Algorithm for Computing the Geometric Quantities of a Square Lattice Polymer. J. Korean Phys. Soc. 73, 1808–1813 (2018). https://doi.org/10.3938/jkps.73.1808

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3938/jkps.73.1808

Keywords

Search

Navigation