## 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 language | English |
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Pages (from-to) | 313-318 |

Number of pages | 6 |

Journal | Random Operators and Stochastic Equations |

Volume | 12 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Analysis
- Statistics and Probability

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