### ANNEALED IMPORTANCE SAMPLING FOR ISING MODELS WITH MIXED BOUNDARY CONDITIONS

Lexing Ying

1. Department of Mathematics, Stanford University, Stanford, CA 94305, USA
• Received:2022-07-26 Revised:2022-11-02 Published:2023-03-14
• Supported by:
This work is partially supported by NSF Grant No. DMS 2011699.

Lexing Ying. ANNEALED IMPORTANCE SAMPLING FOR ISING MODELS WITH MIXED BOUNDARY CONDITIONS[J]. Journal of Computational Mathematics, 2023, 41(3): 526-534.

This note introduces a method for sampling Ising models with mixed boundary conditions. As an application of annealed importance sampling and the Swendsen-Wang algorithm, the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition gradually. The numerical results show that the variance of the sample weights is relatively small.

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