We propose a Monte Carlo method to obtain the thermodynamic functions of Ising systems. We perform a random sampling of spin configurations to determine the degeneracy of the energies of the system, from which an approximant to the partition function is determined. The main advantage of the method over conventional Metropolis lies in the fact that only a single Monte Carlo run is needed to obtain results valid for all temperatures, magnetic fields, and coupling parameters (FM or AFM). As an illustration of the method, we present results for the Ising model in a magnetic field on a 8x8 lattice. The method can be adapted to tackle the random field Ising model (RFIM), the dilute Ising model, and the Ising spin glass, in any spatial dimension.
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Lieu, C., Florencio, J. A novel Monte Carlo simulation method for Ising systems. J Low Temp Phys 89, 565–568 (1992). https://doi.org/10.1007/BF00694088
- Magnetic Field
- Random Sampling
- Monte Carlo Method
- Partition Function
- Magnetic Material