Controlling sign problems in spin models using tensor renormalization

2013/09/25 by Alan Denbleyker, A. Denbleyker, Yuzhi Liu +10 · 65 citations
Mathematics · Physics and Astronomy · #BETA (programming language) #Geometry #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Renormalization #Renormalization group #Scaling #Sign (mathematics) #Spin (aerodynamics) #Statistical physics #Statistics #Tensor (intrinsic definition) #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech #cond-mat.str-el #hep-lat #hep-th

paper · pdf · doi:10.1103/physrevd.89.016008

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 89(1) (American Physical Society) · 8 pages, 9 figures

arxiv created 2013/09/25 · openalex publication_date 2014/01/09 · arxiv updated 2014/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the sign problem for classical spin models at complex \ensuremathβ=1/g₀² on L\ifmmode×\else\texttimes\fiL lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im\ensuremathβ than the reweighting Monte Carlo method. For the Ising model with complex \ensuremathβ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L\ifmmode×\else\texttimes\fiL lattices when the number of states D_s increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

Citations

• Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions
• Fisher’s zeros of quasi-Gaussian densities of states
• The two-dimensionalXYmodel at the transition temperature: a high-precision Monte Carlo study
• Density Matrix Renormalization Group Method for 2D Classical Models
• High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensionalXYmodel
• The critical properties of the two-dimensional xy model
• Ordering, metastability and phase transitions in two-dimensional systems

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• Comparing Tensor Renormalization Group and Monte Carlo calculations for spin and gauge models
• Tensor network analysis of critical coupling in two dimensional ϕ4 theory

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