Abstract:
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.