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Zeros in the complex -plane of 2D Ising block spin Boltzmannians

1998/07/20 by K. Pinn
Mathematics · Physics and Astronomy · #BETA (programming language) #Block (permutation group theory) #Combinatorics #Complex plane #Computer science #Geometry #Ising model #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Physics #Plane (geometry) #Quantum many-body systems #Renormalization #Renormalization group #Spin (aerodynamics) #Spurious relationship #Statistical physics #Statistics #Theoretical and Computational Physics #Transfer matrix #Transformation (genetics) #cond-mat.stat-mech #hep-lat

paper · pdf · doi:10.1088/0305-4470/31/46/012

14 pages, 7 figures

arxiv created 1998/07/20 · openalex publication_date 1998/11/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Effective Boltzmannians in the sense of the block spin renormalization group are computed for the 2D Ising model. The blocking is done with majority and Kadanoff rules for blocks of size . Transfer matrix techniques allow the determination of effective Boltzmannians as polynomials in for lattices of up to blocks. The zeros of these polynomials are computed for all non-equivalent block spin configurations. Their distribution in the complex -plane reflects the regularity structure of the block spin transformation. In the case of the Kadanoff rule spurious zeros approach the positive real -axis at large values of . They might be related to the renormalization group pathologies discussed in the literature.

Citations