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arXiv:2610.25270

Tensor network Monte Carlo study of the J1-J2 Ising model on the square lattice

Wanying Zheng, Tao Chen, Youjin Deng, Wanzhou Zhang

Published Oct 18, 2026• 0 citations
arXivHTMLPDF

Abstract

The frustrated square-lattice J1-J2 Ising model exhibits rich magnetic phases, yet its phase transitions remain difficult to characterize due to critical slowing down in conventional Monte Carlo and truncation errors inherent to tensor renormalization group methods. We develop a tensor-network Monte Carlo (TNMC) algorithm for this frustrated model, which supports both open and periodic boundary conditions. For periodic lattices, we use a sweeping block-update strategy that updates spin blocks while fixing surrounding spins. To boost efficiency, we couple our sampler with histogram reweighting, and test each technique standalone to validate these independent optimizations. We perform extensive finite-size scaling analyses at g=0.55 and g=1.0, extracting apparent critical temperatures and effective thermal exponents from Binder-cumulant data. Our method offers an efficient, nearly bias-free path for large-scale simulations of J1-J2-type frustrated magnets under periodic boundaries and generalizes readily to other frustrated spin lattices.

DOI
10.48550/arxiv.2610.25270

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