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Investigation of One-Dimensional Spin Glass Using Combinatorial Factor Method

Darioush Sharafie, Shahram Ranjbar

Ising model as a simplified model of reality, exhibits phase transition. Combinational factor method is a numerical method which is applied for infinite lattices with a limited number of rows or small m. In this work, we used the combinatorial factor method to find the thermodynamic properties of the spin glass (A1-xBx). For simplicity, we supposed that, the spin glass can be considered as one-dimensional lattice with nearest neighbor interactions. For this model, having an exact combinatorial factor and accordingly the corresponding exact energy, the Helmholtz free energy is minimized. Overall, one dimensional spin glass does not show phase transition as like as one-dimensional Ising model. There are same trends in temperature and entropy in this model, in both constant x and f cases, a same trend was seen for maximum of heat capacity (where f is constant, and Coefficient is interaction energies between the nearest neighbor pair of ii.).