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Progress of Theoretical Physics

Critical Properties of Ising Models Containing Dilute Impurities

Takeo Osawa, K. Sawada

Published Jan 1, 1973• 11 citations
Publisher

Abstract

The correlation functions for the Ising model with one bond defect can be exactly expressed by the ones for the pure Ising model. By using these expressions, the internal energy of the Ising model with dilute impurities is obtained. The critical behaviour of the impure Ising model is discussed and the shift of the critical temperature is determined.

DOI
10.1143/ptp.49.83

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The correlation functions for the Ising model with one bond defect can be exactly expressed by the ones for the pure Ising model. By using these expressions, the internal energy of the Ising model with dilute impurities is obtained. The critical behaviour of the impure Ising model is discussed and the shift of the critical temperature is determined.
We have performed Monte Carlo calculations of the thermodynamic properties of the bond-dilute Ising model on the square lattice. The results are obtained for the magnetization, internal energy, specific heat, and susceptibility for several concentrations of missing bonds. The dependence of the Curie temperature on dilution is in good agreement with the results obtained by other methods. The phase transition is found to remain sharp with the same value of the susceptibility exponent as for the pure Ising model.
High accuracy Monte Carlo simulation results for 1024*1024 Ising system with ferromagnetic impurity bonds are presented. Spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This is not trivial since a critical temperature for the system with impurities is almost two times lower than pure Ising TcT_cTc​. Small deviations from the pure behaviour contradict to some of the competing theories.