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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 , 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 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.