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In this chapter we investigate one-dimensional KCM. Most notably, these include the FA-1f and East models. We present the techniques used to determine the scaling of their characteristic times as \(q\rightarrow 0\) . We familiarise ourselves with the use of test functions, non BP-based canonical paths, combinatorial bottlenecks and bisection in the simplest possible setting. We then move on to FA-2f and general KCM, still in one dimension. These one-dimensional models are not only interesting in their own right, but will also serve as tools for the study of higher-dimensional KCM via renormalisation.

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One-Dimensional Models

  • 章节

  • 发表日期：

    2025年

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  • Ivailo Hartarsky,
  • Cristina Toninelli

摘要

In this chapter we investigate one-dimensional KCM. Most notably, these include the FA-1f and East models. We present the techniques used to determine the scaling of their characteristic times as \(q\rightarrow 0\) . We familiarise ourselves with the use of test functions, non BP-based canonical paths, combinatorial bottlenecks and bisection in the simplest possible setting. We then move on to FA-2f and general KCM, still in one dimension. These one-dimensional models are not only interesting in their own right, but will also serve as tools for the study of higher-dimensional KCM via renormalisation.