A remark on different lattice approximations and continuum limits for φ 4 2-fields

Sergio Albeverio, Song Liang

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Consider the lattice approximation of a φ 4 2-quantum field model with different lattice cutoffs a′ and a in the free and interacting parts, respectively. In [1] it was shown that the corresponding continuum limit measure exists if lim a→0 a′| log a| 5/4 < ∞ and it coincides with the original φ 4 2-field measure if lim a→0 a′ |log a| 2 < ∞. In this paper, a result is given indicating that the new continuum limit measure might be different from the original one if a′ is too big compared with a.

Original languageEnglish
Pages (from-to)313-318
Number of pages6
JournalRandom Operators and Stochastic Equations
Volume12
Issue number4
DOIs
Publication statusPublished - 2004
Externally publishedYes

Keywords

  • φ -model
  • Continuum limits
  • Inequalities
  • Lattice approximation
  • Quantum fields

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability

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