Skip to main content
Log in

Joint Density of States Calculation Employing Wang–Landau Algorithm

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Joint density of states (JDoS), which depends both on energy and another variable like order parameter provides more information than the conventional density of states (DoS) which depend only on energy. Calculation of JDoS requires huge computational time. In this paper we employ two level method to calculate JDoS which requires relatively much less computational time. We demonstrate this method on a two dimensional Ising spin system, lattice spin model of double strand DNA (dsDNA) and Heisenberg ferromagnet.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Wang, F., Landau, D.P.: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86, 2050 (2001)

    Article  ADS  Google Scholar 

  2. Rathore, N., de Pablo, J.J.: Monte Carlo simulation of proteins through a random walk in energy space. J. Chem. Phys. 116, 7225–7230 (2002)

    Article  ADS  Google Scholar 

  3. Suman Kalyan, M., Murthy, K.P.N.: Monte Carlo study of force induced melting of DNA hairpin. Physica A 428, 38–45 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  4. Yamaguchi, C., Okabe, Y.: Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm. J. Phys. A: Math. Gen. 34, 8781 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Zhou, C., Schulthess, T.C., Torbrugge, S., Landau, D.P.: Wang-Landau algorithm for continuous models and joint density of states. Phys. Rev. Lett. 96, 120201 (2006)

    Article  ADS  Google Scholar 

  6. Okabe, Y., Tomita, Y., Yamaguchi, C.: Application of new Monte Carlo algorithms to random spin systems. Comput. Phys. Commun. 146, 63–68 (2002)

    Article  ADS  MATH  Google Scholar 

  7. Jayasri, D., Sastry, V.S.S., Murthy, K.P.N.: Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals. Phys. Rev. E 72, 036702 (2005)

    Article  ADS  Google Scholar 

  8. Mukhopadhyay, K., Ghoshal, N., Roy, S.K.: Monte Carlo simulation of joint density of states in one-dimensional Lebwohl–Lasher model using Wang–Landau algorithm. Phys. Lett. A 372, 3369–3374 (2008)

  9. Tolédano, J.C., Tolédano, P.: The Landau Theory of Phase Transitions. World Scientific publishing Co. Pte. Ltd., Singapore (1987)

  10. Landau, D.P., Tsai, S-H., Exler, M.: A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling. Am. J. Phys. 72, 1294–1302 (2004)

  11. Gervais, C., Wüst, T., Landau, D.P., Xu, Y.: Application of the Wang–Landau algorithm to the dimerization of glycophorin. J. Chem. Phys. 130, 215106 (2009)

    Article  ADS  Google Scholar 

  12. Kumar, Santosh: Random matrix ensembles: Wang-Landau algorithm for spectral densities. EPL 101, 20002 (2013)

    Article  ADS  Google Scholar 

  13. Maerzke, K.A., Gai, L., Cummings, P.T., McCabe, C.: Simulating phase equilibria using Wang-Landau-transition matrix Monte Carlo. J. Phys. 487, 012002 (2014)

  14. Brush, Stephen G.: History of the Lenz-Ising model. Rev. Mod. Phys. 39, 883 (1967)

    Article  ADS  Google Scholar 

  15. Li, M.S., Cieplak, M.: Folding in two-dimensional off-lattice models of proteins. Phys. Rev. E. 59, 970 (1999)

    Article  ADS  Google Scholar 

  16. Go, N., Abe, H.: Noninteracting local-structure model of folding and unfolding transition in globular proteins. I. Formulation. Biopolymers 20, 991–1011 (1981)

  17. Carmesin, I., Kremer, K.: The bond fluctuation method: a new effective algorithm for the dynamics of polymers in all spatial dimensions. Macromolecules 21, 2819–2823 (1988)

    Article  ADS  Google Scholar 

  18. Mishra, G., Giri, D., Li, M.S., Kumar, S.: Role of loop entropy in the force induced melting of DNA hairpin. J. Chem. Phys. 135, 035102 (2011)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

Computations were carried out i) in SHAKTI cluster at Manipal Centre for Natural Sciences, Manipal University ii) at Centre for Modelling, Simulation and Design (CMSD), University of Hyderabad.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Suman Kalyan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalyan, M.S., Bharath, R., Sastry, V.S.S. et al. Joint Density of States Calculation Employing Wang–Landau Algorithm. J Stat Phys 163, 197–209 (2016). https://doi.org/10.1007/s10955-016-1472-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-016-1472-5

Keywords

Navigation