Influence of allowance for cluster interaction on scaling in Fisher's droplet model of phase transitions. The cluster fluctuation model

When the interaction between clusters is taken into account in the multidimensional “droplet” model, the relations obtained between the critical exponents differ from those in the model without interaction: $\sigma=1/(\gamma+2\beta)$, $\tau=2+1/(\delta+1)$. A different approximate expansion is also considered: with respect to fluctuations in the form of “excesses”, which are defined like Mayer groups. This expansion leads to a system of noninteracting clusters with their own scaling and a different value of $\tau$. It is shown that this expansion corresponds to the “droplet” model with interaction, and this confirms the need for and correctness of the allowance for the interaction in it. It is argued that the most probable shape of large clusters is spherical and that the logarithmic exponent $\tau$ is nonuniversal.