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As spins and bonds are decimated, the number of spins coupled to a given spin (or its effective coordination number) becomes larger and larger, which is typical when couplings beyond one dimension are present [see, e.g
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As spins and bonds are decimated, the number of spins coupled to a given spin (or its effective coordination number) becomes larger and larger, which is typical when couplings beyond one dimension are present [see, e.g., Olexei Motrunich, Siun-Chuon Mau, David A. Huse, and Daniel S. Fisher, Phys. Rev. B 61, 1160 (2000)]; thus the number of spins that are coupled to the strongest bond one plans to decimate also grows. However, just like this case to second order we only need to treat a four-spin cluster at a given time.
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Motrunich, O.1
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See, e.g, Addison-Wesley, Reading, MA
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85038321020
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When the sizes of the spins are not uniform, in principle there can be different ways to define the strongest bond; see, e.g., Ref. 10. As we will see later in the present case the majority of the spins remain to be spin-1/2 in all stages of the RG; we thus simply choose to define the strongest bond to be the bond with the largest absolute value of the bond strength, regardless of the sizes of the spins that it couples
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When the sizes of the spins are not uniform, in principle there can be different ways to define the strongest bond; see, e.g., Ref. 10. As we will see later in the present case the majority of the spins remain to be spin-1/2 in all stages of the RG; we thus simply choose to define the strongest bond to be the bond with the largest absolute value of the bond strength, regardless of the sizes of the spins that it couples.
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