Extended Ising model

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Abstract
In this paper we describe a numerical method of solving the local-density mean-field equations of spatially frustrated lattice models. Using techniques of simulated annealing and simultaneous updating of collective modes, we have been able to locate the global minima of a function with many nearby local minima. This approach is applied to an isotropic frustrated lattice model with magnetic field in order to determine the global phase diagram. We also mention a related simulation technique which might be used to replace the traditional single-spin-flip Monte Carlo method. This appears to be a promising way of simulating periodic spatially frustrated lattice Hamiltonians. Finally, some consideration is given to the physical interpretation of a lattice model of microemulsions.

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