A rigorous control of logarithmic corrections in four-dimensional φ{symbol}4 spin systems - II. Critical behavior of susceptibility and correlation length

Takashi Hara, Hal Tasaki

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33 Citations (Scopus)

Abstract

Continuing the analysis started in Part I of this work, we investigate critical phenomena in weakly coupled φ{symbol}4 spin systems in four dimensions. Concerning the critical behavior of the susceptibility and the correlation length (in the high-temperature phase), the existence of logarithmic corrections to their mean field type behavior is rigorously shown (i.e., we prove χ(t)~t- 1 |ln t|1/3, ξ(t)~t-1/2|ln t}|1/6).

Original languageEnglish
Pages (from-to)99-121
Number of pages23
JournalJournal of Statistical Physics
Volume47
Issue number1-2
DOIs
Publication statusPublished - Apr 1 1987
Externally publishedYes

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Critical Phenomena
Spin Systems
Correlation Length
Critical Behavior
Mean Field
Susceptibility
Logarithmic
magnetic permeability

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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AB - Continuing the analysis started in Part I of this work, we investigate critical phenomena in weakly coupled φ{symbol}4 spin systems in four dimensions. Concerning the critical behavior of the susceptibility and the correlation length (in the high-temperature phase), the existence of logarithmic corrections to their mean field type behavior is rigorously shown (i.e., we prove χ(t)~t- 1 |ln t|1/3, ξ(t)~t-1/2|ln t}|1/6).

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