Examines the behavior of partition functions in correlated Gaussian environments, indicating critical insights into disorder relevance.
We consider a pinning model in correlated Gaussian random environments. For the model that is disorder relevant, we study its intermediate disorder regime and show that the rescaled partition functions converge to a non-trivial continuum limit in the Skorohod setting and in the Stratonovich setting, respectively. Our results partially confirm the Weinrib–Halperin prediction for disorder relevance/irrelevance.
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Li et al. (2026) studied this question.
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