Math @ Duke

Publications [#361468] of Holden Lee
Papers Published
 Helmuth, T; Lee, H; Perkins, W; Ravichandran, M; Wu, Q, Approximation algorithms for the randomfield Ising model
(August, 2021)
(last updated on 2022/05/22)
Abstract: Approximating the partition function of the ferromagnetic Ising model with
general external fields is known to be #BIShard in the worst case, even for
boundeddegree graphs, and it is widely believed that no polynomialtime
approximation scheme exists. This motivates an averagecase question: are there
classes of instances for which polynomialtime 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 polynomialtime
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 zerofree region, and
cause worstcase analyses of Glauber dynamics to fail. The analysis of our
algorithm is based on percolation on a selfavoiding walk tree.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

