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Proceedings of the Highly Frustrated Magnetism Conference 2000, edited by M. J. P. Gingras (unpublished).
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in Proceedings of the Highly Frustrated Magnetism 2000 Conference (Ref. 1), cond-mat/0010301 (unpublished)
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I. Syozi, in Phase Transitions and Critical Phenomena (Academic, London, 1972), Vol. 1, Chap. 7, pp. 269–330.
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Syozi, I.1
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85038301352
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It is important to stress that this single axis Ising spin system cannot occur in a pyrochlore lattice, as it is incompatible with the cubic symmetry of the spatial group. However, it is a very instructive example, and will prove to be useful for testing the accuracy of the results presented in this work
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It is important to stress that this single axis Ising spin system cannot occur in a pyrochlore lattice, as it is incompatible with the cubic symmetry of the spatial group. However, it is a very instructive example, and will prove to be useful for testing the accuracy of the results presented in this work.
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This is the case even if we consider the smallest possible clusters. See, for example, I. P. Fittipaldi and D. F. de Alburquerque, J. Magn. Magn. Mater. 104-107, 236 (1992), where they studied the Ising model with bond dilution in both the simple square and kagomé lattices in the EFRG framework by using clusters of one and two spins, respectively.
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Another possible definition of the scaling factor we can use consists of calculating from Eq. (79) the value of l that leads to the exact value of (Formula presented) for the standard Ising model and making use of this value to estimate the corresponding magnetic critical exponent. The values of l obtained in this way are (Formula presented) and (Formula presented) for the kagomé and pyrochlore lattices, respectively. The corresponding magnetic critical exponents are (Formula presented) and (Formula presented) for the standard Ising model in the kagomé and pyrochlore lattices, respectively, and (Formula presented) and (Formula presented), for the 2D spin ice and the 3D spin ice, respectively
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Another possible definition of the scaling factor we can use consists of calculating from Eq. (79) the value of l that leads to the exact value of (Formula presented) for the standard Ising model and making use of this value to estimate the corresponding magnetic critical exponent. The values of l obtained in this way are (Formula presented) and (Formula presented) for the kagomé and pyrochlore lattices, respectively. The corresponding magnetic critical exponents are (Formula presented) and (Formula presented) for the standard Ising model in the kagomé and pyrochlore lattices, respectively, and (Formula presented) and (Formula presented), for the 2D spin ice and the 3D spin ice, respectively.
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Even though, this is only the case for very special cases, such as the ones considered in this work, because spin-ice systems with arbitrary unitary vectors are, in general, incompatible with the symmetries of the crystalline lattice
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Even though, this is only the case for very special cases, such as the ones considered in this work, because spin-ice systems with arbitrary unitary vectors are, in general, incompatible with the symmetries of the crystalline lattice.
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