Chap.3 A Tour through Critical Phenomena. Youjin Deng 09.12.5. Three Important classes: Liquid-gas, magnet, binary fluid or alloy Let start with the phase diagram of water. Phenomena observed near the critical point are referred to as Critical phenomena.
Let start with the phase diagram of water
Phenomena observed near the critical point are referred to as
And the relation
???: 1), Definitions of Quantities (more rigorous) 2), Experimental Pictures
combinations of them have more fundamental significance,
For each site i, using the mean field approximation,
the Hamiltonian becomes
The partition sum:
Magnetization in zero field (h=0)
When K<Kc and h finite
Note that, Mean field theory does not in general give a correct description of critical behavior, since that nonuniform spin configurations have been excluded, thus, the effect of fluctuations has been ignored.
Although, unsatisfactory in many aspects, the mean field theory captures a few important features of critical phenomena, it gives us a qualitative understanding of the major mechanisms behind the critical phenomena.
This table summarizes the experimental values of the critical exponents as well as
the results from some theoretical models. We can see that the scaling laws seem
to be universal, but the individual exponents show definite deviations from truly
1>the lattice dimensionality
2>the spin dimensionality
3>the fallout exponent p of the long range interactions such as