= Solution
The <mean-field approximation> suppresses correlated order-parameter fluctuations. Near a <continuous phase transition>, the <correlation length> diverges and long-wavelength fluctuations become increasingly important. The <Ginzburg criterion> therefore fails in sufficiently low dimension, and the interacting <renormalization-group fixed point> changes the mean-field exponents. For the tricritical $m^6$ theory the <upper critical dimension> is three: below $d=3$ the exponents are generally non-mean-field, while at $d=3$ one expects logarithmic corrections to mean-field scaling.
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