## Publications [#361468] of Holden Lee

Papers Published

1. Helmuth, T; Lee, H; Perkins, W; Ravichandran, M; Wu, Q, Approximation algorithms for the random-field Ising model (August, 2021)
(last updated on 2022/07/03)

Abstract:
Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and it is widely believed that no polynomial-time approximation scheme exists. This motivates an average-case question: are there classes of instances for which polynomial-time approximation schemes exist? We investigate this question for the random field Ising model on graphs with maximum degree \$\Delta\$. We establish the existence of fully polynomial-time approximation schemes and samplers with high probability over the random fields if the external fields are IID Gaussians with variance larger than a constant depending only on the inverse temperature and \$\Delta\$. The main challenge comes from the positive density of vertices at which the external field is small. These regions, which may have connected components of size \$\Theta(\log n)\$, are a barrier to algorithms based on establishing a zero-free region, and cause worst-case analyses of Glauber dynamics to fail. The analysis of our algorithm is based on percolation on a self-avoiding walk tree.