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where y is some constant. This may be justified physically as follows: The magnetic moments in the system are strongly correlated within a correlation length, which tends to infinity as t ~ o. Thus, there is a natural tendency for very large blocks of magnetic moments to line up. The effect of an external field is thereby magnified, with a magnification factor proportional to some power of the correlation length. Hence we expect H to occur only in the combination He. Making the replacement

(16.41)

Using trendlines when the price action is neat and well-de ned is pretty simple. When prices don t bounce precisely off trendlines and the price behavior is mushy with respect to support and resistance levels, it is far more challenging. Although, by de nition, there aren t any absolute rules when dealing with this ambiguous behavior, it is still helpful to look at some past, real-life examples to see how they played out. The S&P 600, showed in Figure 7.52, enjoyed a long, persistent uptrend. There are two trendlines shown, both of them ascending. The higher trendline was violated about halfway along the graph, and although it brie y moved above this line later, it fell once more, clearly showing this uptrend was history. The line beneath it had a similar result, although in the opposite

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This is called a "scaling form" of the correlation function. The quantity ~ is sometimes called the "gap exponent," because (16.41) gains a factor t a when integrated with respect to H. It is instructive to derive the scaling laws again from the scaling forms. By the fluctuation-dissipation theorem and (16.39), we have

x/~,

~d-p _

Itl- (2-1))

(16.42)

which yields y = v(2 - 1/), Fisher's scaling law. In a similar manner, when H = 0, we use the fluctuation-dissipation theorem together with (16.41) to deduce

(16.43)

Integrating this with respect to H gives the scaling form of the equation of state:

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sense. In this instance, support held for virtually the entire graph, although it was brie y violated. But both of these trendlines tell the same story: Even though price action can move to the other side of a line, so long as this violation is brief, and provided that the prices resume obeying the trendline afterward, the trendline still does have meaning. There s no doubt that the validity of the trendline is diminished with any violation, but it is not eliminated completely. An extremely interesting example of this is shown with Raven Industries (Figure 7.53). From 2000 through 2004, ve whole years, the prices steadily climbed, never piercing the ascending support line. Early in 2005, when the prices broke the trendline, it did not signal a trend change. Instead, the trend continued upward, simply shifted downward several price points. What s remarkable about this graph is how the prices clung to the former support line, crossing above and below it many times, but generally sticking rigidly to the line as if it were a magnet. The softening of a trend s direction can take the form of a price reduction, as with Raven Industries, or the form of a reduction in the steepness of a trend, such as with Figure 7.54. In this case, the NASDAQ 100 market violated its major ascending trendline, but over time it continued a softer

(16.44)

(16.45)

Integrating (16.44) with respect to H yields the scaling form of the Gibbs free energy:

G - Itl2t.-y~ (H/ltla)

(16.46)

0, we have G - ItI 2a -r, and hence C - ItI 2a - y- 2 - ItI 2/1+y-2

(16.47)

which gives a + 2{3 + y = 2, Rushbrooke's law. At t = and H =1= 0, the order parameter is assumed to be finite. Therefore the function .A in (16.44) must have the following behavior:

FIGURE 7.53 After RAVN breaks through its trendline, the price seems to cling to the line as a median instead of either support or resistance.

.A (H/ltla)_IW+a-2 = Itl-/1

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