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In this sense, the (antiferromagnetic) (Formula presented) chain is exceptional; it always satisfies (Formula presented) for all magnetization and lies in the region of unconditional localization. The case with (Formula presented) is in a sense marginal
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The so-called flow equation for the renormalized coupling (Formula presented) [see Eq. (2) of Ref. 36] is replaced by (Formula presented)and an argument similar to that given in Ref. 14 leads to the conclusion that the system enters the random-singlet phase. Recall that special cases with (Formula presented) and 1 correspond to the model treated in Refs. 14 and 36, respectively
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The so-called flow equation for the renormalized coupling (Formula presented) [see Eq. (2) of Ref. 36] is replaced by (Formula presented)and an argument similar to that given in Ref. 14 leads to the conclusion that the system enters the random-singlet phase. Recall that special cases with (Formula presented) and 1 correspond to the model treated in Refs. 14 and 36, respectively.
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At least for multicomponent models known so far, there is always a region where a description based on the single-component TL model is valid. For such a region, we can still use the method presented here
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At least for multicomponent models known so far, there is always a region where a description based on the single-component TL model is valid. For such a region, we can still use the method presented here.
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