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above a trendline is shown with the S&P 400 MidCap index in Figure 7.47. In this case, prices broke below the trendline and stayed there for a full month before breaking above the former support line again. From there, it regained its former bullish disposition and soared another 20 percent. Interestingly, in spite of the damage caused to the support line by the price action being beneath it for a full month, the prices still seemed to have a healthy respect for this as a support line once it regained its composure. A close-up view of this month-long hiatus from support levels is illustrated with Figure 7.48. It is interesting to see how, on a day-by-day basis, price actions behave with respect to the supporting trendline. More often than not, trendline breaks do indicate directional change, so let us turn our attention to some chart examples that show this concept in action.

(Im(k)1 2 ) =

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(16.14)

This gives the Fourier transform of the correlation function in "Ornstein-Zernike form." Taking the inverse Fourier transform we obtain

r where ~ = !C l/C 2 is the "correlation length," a measure of the spatial memory. Experimentally ~ diverges at the critical point. The correlation function then becomes l/r, which does not contain any characteristic length. We shall derive r in d dimensions in the next chapter, under essentially the same assumptions in different guises (see (17.46) and (17.91 . From (16.7) we can rewrite the order parameter more explicitly in the form

r(r)

(16.15)

(16.16)

The last relation is obtained under the assumption that the system is transla-

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The chart in Figure 7.49 is worth careful study. On the chart, ve separate trendlines are shown, each of which lasts a signi cant period in some cases, many years. There are a couple of fascinating things about this graph, which help drive home the power of trendline analysis. First, there are ve clear directional trends, and they toggle to a different direction each time: up, down, up, down, and then up again (although this last uptrend is violated on the extreme right portion of the graph, suggesting that perhaps even a sixth line is in the process of being formed). Second, each trendline has multiple touch points on the price data. In spite of all of the events that happened during the 11 years of this graph economic booms and busts, changes in Presidential administrations, dozens of earnings releases for this stock, hundreds of news releases, and all the ups and downs of the stock market in general the price action can still be clearly bounded by a series of simple, straight lines.

tionally invariant. Assume that the magnetic field H is coupled linearly to the order parameter:

(16.17)

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(16.18)

Jd r r(r)

(16.19)

This is a special case of a general relation known as the" fluctuation-dissipation theorem." We have encountered examples of this in the relation between the heat capacity and energy fluctuations (Eq. (7.14)), and in the relation between the compressibility and density fluctuations (Eq. (7.43)).

The critical exponents describe the nature of the singularities in various measurable quantities at the critical point. Six are commonly recognized, denoted by (at this point) a rather dull list of Greek letters: a, /3, y, 8, T/, P. Denote the critical temperature by Tc ' and introduce the quantity

these lines is very similar to the application of retracements. Examine the chart for Hansen Natural (symbol HANS) in Figure 13.17. To draw this Fibonacci fan, a user would:

t= - - -

(16.20)

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