Block Spin Methods
The critical properties of a system depend not on short-distance
details, but only on the nature of long-wavelength fluctuations.
This suggests that one should do away with the irrelevant degrees
of freedom by continuing a coarse-graining procedure (through which
the details on an atomic scale get averaged out) to ever larger
distance scales, until one reaches the correlation length.
Kadanoff first introduced this idea in terms of "block spin" transformations
in Ising models. The idea here is that near the critical point the spins
should act in concert in large blocks. Thus the important degree of freedom
are the average spins of the blocks, rather than the original individual
spins. One should describe the systems in terms of an effective Hamiltonian
involving only the "block spins".
References and further reading
- K. Huang, Statistical Mechanics (Wiley, 1987) 2ed.
- L.P. Kadanoff, Physics 2 (1966) 2
- G. Mack, Multigrid Methods in Quantum Field Theory, Cargese Lectures
1987, in: Nonperturbative Quantum Field Theory (Plenum, NY, 1989)
Marcus Speh, 22-12-94
Bernhard Weininger, 29-12-94