Beyond Windability: An FPRAS for The Six-Vertex Model

Zhiguo Fu; Junda Li; Xiongxin Yang

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arXiv · 2202.02999

Beyond Windability: An FPRAS for The Six-Vertex Model

Zhiguo Fu·Junda Li·Xiongxin Yang

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Abstract

The six-vertex model is an important model in statistical physics and has deep connections with counting problems. There have been some fully polynomial randomized approximation schemes (FPRAS) for the six-vertex model [30, 10], which all require that the constraint functions are windable. In the present paper, we give an FPRAS for the six-vertex model with an unwindable constraint function by Markov Chain Monte Carlo method (MCMC). Different from [10], we use the Glauber dynamics to design the Markov Chain depending on a circuit decomposition of the underlying graph. Moreover, we prove the rapid mixing of the Markov Chain by coupling, instead of canonical paths in [10].

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BibTeX RIS

Zhiguo Fu, Junda Li, Xiongxin Yang. 2022-02-07. Beyond Windability: An FPRAS for The Six-Vertex Model. https://arxiv.org/abs/2202.02999

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