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.

• 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
• The upper critical dimension of field theories can be found with the help of a program, which also explains the mathematical background: freewarefiles.com/Kanon_program_83832.html – Richard Dengler Apr 14 at 19:42

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