Block model for the XY-type Landau–Ginzburg–Wilson Hamiltonian with random temperature

The phase fluctuation near the saddle point solution of the XY-type Landau–Ginzburg–Wilson Hamiltonian with random temperature is studied. Through some examples, it is argued that the systems are self-organized into blocks, which are coupled as a XY model with random bond. The couplings obtained in this way agree with those by the domain wall method.