Author

Ru-Pei Yan

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Preprint Sep 2026

Correlation comparisons and critical curves for disordered XY models

We prove a lower comparison for disorder-averaged ferromagnetic XY correlations: independent nonnegative random couplings $K_e$ can be replaced by $-\frac12\log\mathbb{E}e^{-2K_e}$. Ginibre's inequality makes each normalized correlation convex in $1-e^{-2K_e}$, so conditional Jensen and thinning compare Bernoulli bond...

Ru-Pei Yan · 0 citations

Preprint Oct 2026

Upper deviations of the Sherrington-Kirkpatrick free energy: the fifth-order law and the onset of constrained Parisi measures

Let $Z_N$ be the partition function of the Sherrington-Kirkpatrick model at inverse temperature $\beta>1$. Replica theory (Kondor near the critical temperature, Parisi and Rizzo at all temperatures) predicts that the probability that $N^{-1}\log Z_N$ exceeds its typical value by $\delta$ decays like $\exp(-Na\delta^{6/...

Ru-Pei Yan · 0 citations

Preprint Sep 2026

Positive-temperature spin-glass order on the three-dimensional Migdal-Kadanoff lattice

We study the Ising spin glass with independent, identically distributed couplings on the diamond hierarchical lattice with $n$ branches, of effective dimension $1+\log_2 n$; $n=4$ is the Migdal-Kadanoff lattice of $\mathbb{Z}^3$. For $n\ge4$ and every coupling law with a bounded density we prove that at sufficiently lo...

Ru-Pei Yan · 0 citations

Preprint Sep 2026

Uniform displacement bounds and Gibbs limits for periodic one-dimensional Riesz gases

For the neutral periodic one-dimensional Riesz gas with pair potential locally $-|x|^a$, $0<a<1$, we prove a particle-displacement variance bound of order $\beta^{-1}$, uniformly in the number of particles. Log-concavity also gives exponential displacement tails. Every stationary periodic thermodynamic limit is simple,...

Ru-Pei Yan · 0 citations

Preprint Sep 2026

Towards the spin-glass transition in finite dimensions via blue percolation

We prove blue percolation in the Chayes-Machta-Redner representation of the zero-field Edwards-Anderson spin glass in finite dimensions. For fixed symmetric iid couplings with $0<m=\mathbb{E}|J|<\infty$, the first blue-percolation inverse temperature $\beta_{\mathrm{b}}(d)$ satisfies $2dm\,\beta_{\mathrm{b}}(d)\to1$ as...

Ru-Pei Yan · 1 citation