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We point out that in a recent paper [, 10.1007/s10955-009-9758-5] an alternative method for evaluating such two-point correlations of the order parameter, based on the resolution of a pair of Toda-type nonlinear differential equations, has been put forward.
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The fictitious temperature β k defined in Eq. depends on mode k also at criticality, since it is obtained by equating the contribution to the total energy due to a single-mode population. Therefore in principle there is no connection with the effective thermodynamic temperature β of Eq. This is the case even at Γ c, where the system exhibits a true thermal behavior in the sense of standard statistical ensembles.
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