# upper critical dimension in field theory

Is there field theory which describe a second order phase transition without upper critical dimension ? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.

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You need a way to declare that two field theories in different dimensions are "the same". There are natural ways to do this for simple examples, but it is easy to make up a model where there is no upper critical dimension because you extrapolate wrong. –  Ron Maimon Apr 28 '12 at 5:32
@PanAkry : Do you know that you can "accept" an answer by clicking the green tick next to it? It's not necessary if you're not satisfied with the answer, but please go through your questions and check if there are any that have correct answers in need of an accept. Thanks! –  Manishearth May 7 '12 at 6:09
Thanks @Manishearth for pointing that out to PanAkry, I was just about to leave the same 'citizenship patrol' comment ;) –  New Alexandria Dec 29 '12 at 23:54

$$S= \int |q|^{2n} |\phi|^2 + \lambda \phi^4 d^n x$$