Open Access
Subscription Access
Investigation of Ising model on square lattice with the effect of Second nearest neighbour interaction
We have investigated Ising like system on two dimensional square lattice with the effect of second nearest neighbour interactions. This system represents ferromagnetic material and it analyzed by Monte-Carlo technique. We have allowed the system to evolve under the Metropolis algorithm (Boltzmann technique) and the thermodynamic observables were calculated. The density of states also determined by using the Wang-Landau algorithm which is typically a non-Boltzmann Monte-Carlo technique. The thermodynamic observables were computed from the converged density of states. The transition temperature found to be changed when the second nearest neighbour was altered. The calculated density of states, average energy (internal energy) and the specific heat capacity have been plotted and discussed.
Keywords
Monte-Carlo, Ising model, Metropolis, Wang-Landau.
User
Font Size
Information
- D. P. Landau and K. Binder, A Guide to Monte Carlo Methods in Statistical Physics, Cambridge University Press, Cambridge, England (2000).
- N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, Journal of Chemical Physics, 21, 1087 (1953).
- F. Wang and D. P. Landau, Efficient, multiple-range random walk algorithm to calculate the density of states, Phy. Rev. Lett, 86, 2050 (2001).
- F. Wang and D. P. Landau, Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram, Phys. Rev. E, 64, 056101 (2001).
- A. K. Murtazaev, M. K. Ramazanov and M. K. Badiev, Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice, Solid State Phenomena, 215, 17-21 (2014).
- Chenggang Zhou, T. C. Schulthess, Stefan Torbrugge and D. P. Landau, Wang-Landau Algorithm for Continuous Models and Joint Density of States, Phy. Rev. Lett, 96, 120201 (2006).
- N. Rathore, J. J. de Pablo, Monte Carlo simulation of proteins through a random walk in energy space. J. Chem. Phys. 116, 7225-7230 (2002).
- M. Suman Kalyan, K. P. N. Murthy, Monte Carlo study of force induced melting of DNA hairpin. Physica A, 428, 38-45 (2015).
- D. Jayasri, V. S. S. Sastry, K. P. N Murthy, Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals. Phys. Rev. E, 72, 036702 (2005).
- K. Mukhopadhyay, N. Ghoshal, S. K. Roy, 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).
Abstract Views: 175
PDF Views: 0