Nonlocal mode-coupling interactions and phase transition near tricriticality

Employing Wilson's renormalization group scheme, we investigate the critical behaviour of a modified Ginzburg-Landau model with a nonlocal mode-coupling interaction in the quartic term. Carrying out the calculations at one-loop order, we obtain the critical exponents in the leading order of $ϵ=4-d-2\rho$, where ρ is an exponent occurring in the nonlocal interaction term and d is the space dimension. Interestingly, the correlation exponent η is found to be non-zero at one-loop order and the ϵ expansion corresponds to an expansion about the tricritical mean-field theory in three dimensions, unlike the conventional ${\Phi }^4$ theory. The ensuing critical exponents are in good agreement with experimental values for samples close to tricriticality. Our analysis indicates that tricriticality is a feature only in three dimensions. (letter)