Correlation comparisons and critical curves for disordered XY models
Abstract
We prove a lower comparison for disorder-averaged ferromagnetic XY correlations: independent nonnegative random couplings Ke can be replaced by −1/2log𝔼e−2Ke. Ginibre's inequality makes each normalized correlation convex in 1−e−2Ke, so conditional Jensen and thinning compare Bernoulli bond densities; two star-wise Jensen passes handle site dilution on bipartite graphs. Together with the phase-existence theorem of Dario and Garban, these comparisons give local Lipschitz regularity of both the averaged algebraic-phase and susceptibility-divergence thresholds throughout the supercritical density intervals on ℤ2. The clean finite-domain criterion of van Engelenburg and Lis also yields explicit finite-size susceptibility lower bounds in a weak-dilution region. For bounded centered bond noise, the possible suppression of the algebraic-phase temperature is at most quadratic in the noise amplitude. Finally, at finite positive thresholds we prove total-variation continuity for bounded iid coupling laws whose essential supremum equals the common support cap, with local Lipschitz control when the reference law has an atom at that cap.
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BibTeX
@misc{pei2026correlation,
title = {{Correlation comparisons and critical curves for disordered XY models}},
author = {Yan Ru Pei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14201},
eprint = {2609.14201},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14201},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Correlation comparisons and critical curves for disordered XY models
AU - Yan Ru Pei
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14201
UR - https://arxiv.org/abs/2609.14201
AB - We prove a lower comparison for disorder-averaged ferromagnetic XY correlations: independent nonnegative random couplings K_e can be replaced by −1/2log𝔼e^−2K_e. Ginibre's inequality makes each normalized correlation convex in 1−e^−2K_e, so conditional Jensen and thinning compare Bernoulli bond densities; two star-wise Jensen passes handle site dilution on bipartite graphs. Together with the phase-existence theorem of Dario and Garban, these comparisons give local Lipschitz regularity of both the averaged algebraic-phase and susceptibility-divergence thresholds throughout the supercritical density intervals on ℤ^2. The clean finite-domain criterion of van Engelenburg and Lis also yields explicit finite-size susceptibility lower bounds in a weak-dilution region. For bounded centered bond noise, the possible suppression of the algebraic-phase temperature is at most quadratic in the noise amplitude. Finally, at finite positive thresholds we prove total-variation continuity for bounded iid coupling laws whose essential supremum equals the common support cap, with local Lipschitz control when the reference law has an atom at that cap.
ER -