Nonlocal mode-coupling interactions and phase transition near tricriticality

Abstract

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 = 4 − d − 2ρ, 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 expansion corresponds to an expansion about the tricritical mean-field theory in three dimensions, unlike the conventional Φ 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.

Reply to Comment on Nonlocal quartic interactions and universality classes in perovskite manganites

“…2(c)] is found to be irrelevant even in the absence of screening, as shown in Ref. [4]. The vertex correction obtained in Ref.…”

“…[4]. An RG calculation [4] with this model could indeed generate tricritical exponents of some perovskite manganite samples satisfactorily. However, this model could not represent satisfactorily the critical exponents of those samples that are away from tricriticality.…”

“…Thus, their model reduces to that of Ref. [4] for u = v = 0 and w = −w. For this choice of parameters, the RG flow equation for the long-range vertex w given in Ref.…”

“…The vertex correction obtained in Ref. [4] can be compared with that of Weinrib and Halperin [5] where the effective Hamiltonian involves a nonlocal quartic interaction term with coupling function g(k) = −v − wk σ−d and a term u|φ α (x)| 4 . Thus, their model reduces to that of Ref.…”

“…In an attempt to capture such a behavior, a model with algebraic decay of interaction with infinite range (m = 0) was considered in Ref. [4]. An RG calculation [4] with this model could indeed generate tricritical exponents of some perovskite manganite samples satisfactorily.…”