Abstract
In this paper, we review the physical concepts of the nonequilibrium techniques for the calculation of free energies applied to magnetic systems using Monte Carlo simulations of different nonequilibrium processes. The methodology allows the calculation of the free energy difference between two different system Hamiltonians, as well as the free energy dependence on temperature and magnetic field for a given Hamiltonian. As an illustration of the effectiveness of this approach, we apply the methodologies to determine the phase diagram of a simple microscopic model, the degenerate Ising model. Our results show very good agreement with those obtained from analytical (theoretical) methods.
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References
Adkins, C.J.: Equilibrium Thermodynamics, 3rd edn. Cambrigde University Press, Cambrigde (1983)
Baxter, R.J.: Exactly Solved Models in Statistical Mechanics. Academic Press, Cambridge (1982)
Brito, B.G.A., Antonelli, A.: Efficient method to include nuclear quantum effects in the determination of phase boundaries. J. Chem. Phys. 137, 034111 (2012)
Cajahuaringa, S., Antonelli, A.: Stochastic sampling of the isothermal-isobaric ensemble: phase diagram of crystalline solids from molecular dynamics simulation. J. Chem. Phys. 149, 064114 (2018)
Castellano, G.: Thermodynamic potentials for simple magnetic systems. J. Magn. Magn. Mater. 260, 146 (2003)
Coey, J.M.D.: Magnetism and Magnetic Materials. Cambridge University Press, Cambridge (2010)
de Koning, M.: Optimizing the driving function for nonequilibrium free-energy calculations in the linear regime: a variational approach. J. Chem. Phys. 122, 104106 (2005)
de Koning, M., Antonelli, A.: Adiabatic switching applied to realistic crystalline solids: Vacancy-formation free energy in copper. Phys. Rev. B 55, 735 (1997)
de Koning, M., Antonelli, A., Yip, S.: Optimized free-energy evaluation using a single reversible-scaling simulation. Phys. Rev. Lett. 83, 3973 (1999)
de Koning, M., Cai, W., Antonelli, A., Yip, S.: Efficient freeenergy calculations by the simulation of nonequilibrium processes. Comput. Sci. Eng. 2, 88–96 (2000)
de Koning, M., Antonelli, A., Yip, S.: Single-simulation determination of phase boundaries: a dynamic clausius-clapeyron integration method. J. Chem. Phys. 115, 11025 (2001)
Ferdinand, A.E., Fisher, M.E.: Bounded and inhomogeneous Ising models. I. specific-heat anomaly of a finite lattice. Phys. Rev. 185, 832 (1969)
Freitas, R., Asta, M., de Koning, M.: Nonequilibrium free-energy calculation of solids using lammps. Comput. Mater. Sci. 112, 333–341 (2016)
Frenkel, D., Smit, B.: Understanding Molecular Simulation: From Algorithms to Applications, 2nd edn. Academic Press, Cambridge (2002)
Garcez, K.M.S., Antonelli, A.: Pressure effects on the transitions between disordered phases in supercooled liquid silicon. J. Chem. Phys. 135, 204508 (2011)
Harris, R.: A study of first- and second-order phase transitions using monte carlo simulations in the micro-canonical ensemble. Phys. Lett. A 111, 299 (1985)
Miranda, C.R., Antonelli, A.: Transitions between disordered phases in supercooled liquid silicon. J. Chem. Phys. 120, 11672 (2004)
Paula Leite, R., Freitas, R., Azevedo, R., de Koning, M.: The uhlenbeck-ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations. J. Chem. Phys. 145, 194101 (2016)
Pessoa, R., de Koning, M., Vitiello, S.A.: Zero-point vacancy concentration in a model quantum solid: a reversible-work approach. J. Stat. Phys. 134, 769 (2009)
Pippard, A.: Elements of Classical Thermodynamics for Advanced Students of Physics. Cambridge University Press, Cambridge (1957)
Planes, A., Vives, E.: Entropic formulation of statistical mechanics. J. Stat. Phys. 106, 827–850 (2002)
Ramírez, R., Herrero, C.P., Antonelli, A., Hernández, E.R.: Path integral calculation of free energies: Quantum effects on the melting temperature of neon. J. Chem. Phys. 129, 064110 (2008)
Schebarchov, D., Schulze, T.P., Hendy, S.C.: Degenerate ising model for atomistic simulation of crystal-melt interfaces. J. Chem. Phys. 140, 074704 (2014)
Watanabe, M., Reinhardt, W.P.: Direct dynamical calculation of entropy and free energy by adiabatic switching. Phys. Rev. Lett. 65, 3301 (1990)
Acknowledgements
We gratefully acknowledge support from the Brazilian agencies CNPq, CAPES, and FAPESP under Grants #2010/16970-0, #2013/08293-7, and #2016/23891-6. The calculations were performed at CCJDR-IFGW-UNICAMP and at CENAPAD-SP in Brazil.
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Cajahuaringa, S., Antonelli, A. Nonequilibrium Free Energy Methods Applied to Magnetic Systems: The Degenerate Ising Model. J Stat Phys 175, 1006–1021 (2019). https://doi.org/10.1007/s10955-019-02267-7
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DOI: https://doi.org/10.1007/s10955-019-02267-7