Critical two-point correlation functions and "equation of motion" in the phi⁴ model

2015/11/18 by J. Kaupuzs, J. Kaupužs, Kaupuzs, J.
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum chaos and dynamical systems #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.1511.05764

15 pages, 3 figures

arxiv created 2015/11/18 · openalex publication_date 2015/11/18 · arxiv updated 2015/11/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Critical two-point correlation functions in the continuous and lattice phi⁴ models with scalar order parameter phi are considered. We show by different non-perturbative methods that the critical correlation functions <phiⁿ(0) phi^m(x)> are proportional to <phi(0) phi(x)> at |x| --> infinity for any positive odd integers n and m. We investigate how our results and some other results for well-defined models can be related to the conformal field theory (CFT), considered by Rychkov and Tan, and reveal some problems here. We find this CFT to be rather formal, as it is based on an ill-defined model. Moreover, we find it very unlikely that the used there "equation of motion" really holds from the point of view of statistical physics.

Citations

• Corrections to finite--size scaling in the phi⁴ model on square lattices
• The Epsilon-Expansion from Conformal Field Theory

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