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be thinking the same thing: If I can just get out of this at breakeven, I ll be happy. So the sellers are lined up, ready to pounce. Price movement after a stock sinks beneath a rounded top can be devastating. This can be good for you in two ways: if you are long the stock, it s a strong indication that you had better get out. If you have no position in the stock, you might even consider shorting it or buying puts on it. (Actually, if you re long the stock, you would be wise to set a stop-loss order just beneath the support level so that you needn t monitor the stock throughout the trading day). A stock s break beneath support can be fast, as illustrated in Figure 9.22, in which the stock fell by a third in just one day. However, piercing support is often just a precursor of more declines to come. For an example of this, examine the chart for OMG in Figure 9.23. The support level for this stock was about $42.50. It had already fallen from $72.50 (and it should be noted here that just as you should not shy away from a stock because it has gone up too much in price when it breaks above resistance, you should likewise not assume that a stock has nished falling in price when it breaks beneath support just because it has already fallen a lot). The stock traded for over a week just beneath its former support line. This would give owners of the stock ample opportunity to get out as well as give newcomers to the stock an opportunity to sell it short.

(18.34)

where N' = b-dN. The same function g appears in both (18.33) and (18.34) because E { s} and E'{s'} are the same functions except for the values of the

"The reason is that (18.18) is the most general form of the Hamiltonian whether we are dealing wi th the original spins or the block spins.

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g(K)

p.(K) + b-dg(K ' )

(18.35)

This, together with (18.32), describes how the system behaves under an RG transformation, which increases the unit of length by a factor b.

Let K(n) denote the coupling constants resulting from n successive applications of a given RG transformation. These coupling constants are given by the recursion relation (18.36)

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FIGURE 9.23 OM Group (symbol OMG) fell so swiftly after this rounded top that some might think the symbol stood for Oh My God.

It is important to note that R is independent of n, a fact that can be proven by constructing R formally through (18.22). A fixed point K * of the map R is defined by

K*=R(K*)

(18.37)

We assume that K(n) approaches a fixed point as n ---) 00.* The Hamiltonian E * corresponding to K * is called the fixed-point Hamiltonian. A fixed point could be physically significant, because it is a point at which the system becomes invariant under a change of length scale. That means the correlation length is either 0 or 00. The latter corresponds to a critical point, which is the physically interesting case. The case with zero correlation length, as we have encountered in the one-dimensional Ising model, corresponds to infinite temperature, and usually can be recognized and rejected. We now investigate the behavior of the system near a fixed point, which we assume to correspond to a critical point. Subtracting (18.37) from (18.36), we have K(n+l) - K* = R(K(n ) - K* (18.38) Assuming n to be very large we can make the linear approximation

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R(K(n )

R(K*) + W(K(n) - K*)

(18.39)

(18.40)

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