because it is extensive. Thus we can find that the thermal disturbance is relatively small. Especially, for the thermodynamic
limit L → ∞, it becomes negligible. In the present study, we have assumed that the thermal noises directly affect the spins
on surface of the system, ∂Ω, and they contribute gradually to the interior spins of the cluster Ω through the internal interactions.
Under these assumptions, we have shown by Eq. (31) that the thermal noises can be reduced into the effective
interaction between the surface spins of H0 and H˜
0. These perspectives of dissipative systems correspond to the fact that
the interaction between the system and the heat bath is relatively very small but not zero, and this interaction leads the
system to equilibrium states.