Year: 2025
Type: preprint
Abstract: Spin systems form an important class of undirected graphical models. For two Gibbs distributions $μ$ and $ν$ induced by two spin systems on the same graph $G = (V, E)$, we study the problem of approximating the total variation distance $d_{TV}(μ,ν)$ with an $ε$-relative error. We propose a new reduction that connects the problem of approximating the TV-distance to sampling and approximate counting. Our applications include the hardcore model and the antiferromagnetic Ising model in the uniqueness regime, the ferromagnetic Ising model, and the general Ising model satisfying the spectral condition. Additionally, we explore the computational complexity of approximating the total variation distance $d_{TV}(μ_S,ν_S)$ between two marginal distributions on an arbitrary subset $S \subseteq V$. We prove that this problem remains hard even when both $μ$ and $ν$ admit polynomial-time sampling and approximate counting algorithms.
Source: arXiv (Cornell University)
Authors: Feng, Weiming, Liu, Hongyang, Yang, Minji
Institutions: University of Hong Kong, Nanjing University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407384948