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


Marcus Speh, 22-12-94
Bernhard Weininger, 29-12-94