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Free Energy Differences for the 2D-Ising Model from Non-Equilibrium Work Theorems

, , and . Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)

Abstract

The two-dimensional Ising model is studied under the influence of an external magnetic field by means of Monte Carlo simulations. Of special interest is the work which is performed when the field is switched on or off. Traditionally this work is calculated by means of thermodynamic integration which requires a large number of simulation steps in order to move the system from the initial to the final state through equilibrium states. In the present work, non-equilibrium simulations are performed, where the field is switched on or off in a small number of steps. Additionally the system is allowed to relax for one Monte Carlo step between two successive magnetic field strengths. By measuring the work performed in each non-equilibrium experiment, a distribution function for the work is obtained. Calculations were carried out below and above, as well as close to the critical temperature $T_c$. In addition, different rates for the switching process of the magnetic field were studied. In order to calculate free energy differences in the system, the work distribution functions were used to apply the Jarzynski and Crooks fluctuation theorems. Both were verified by comparing results to those from thermodynamic integration. It is found that free energy differences agree very well within error bars. However, it is found that the Crooks fluctuation theorem provides a significantly faster method for the evaluation of free energy differences in the system with respect to the Jarzynski equality. As expected, for temperatures far from $T_c$ the convergence of the results is faster than for $TT_c$, where a slower switching rate is needed.

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