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of resistance. From that point, the stock moved up about 500% in the course of a year. The concept of how resistance can change into support (and vice versa) is critical to your understanding of reading a chart. Any sort of line be it a trendline, a channel, a horizontal line has two faces to it: support and resistance. Once prices cross a line, the nature of that line changes. As you will learn later in the book, if a price crosses a line more than once, the line becomes meaningless and should probably be deleted. Let s take another look at resistance to see how valuable it is to have an awareness of price behavior at certain levels. Figure 1.4 shows the stock for Chesapeake Energy (symbol CHK) over a period of about half a year. Early on, the price was blasting skyward to a new high, then it slumped down through August. It then regained its footing and mounted a new assault on higher prices, but it was repelled again at about the same level. A couple of months later, in November, a third attempt was made to push past the $34 barrier, but it failed a third time. You can imagine the frustration and exasperation of the owners of this stock as they kept seeing their stock getting shoved away from higher prices. What the market was telling the owners of this stock was: You re not going to go any higher. The supply of stock (those selling it) was creating what is known as overhead resistance. Perhaps some people who bought

*L. Onsager, Phys. Rev. 65, 117 (1944); B. Kaufmann, Phys. Rev. 76, 1232 (1949). The present account follows Kaufmann's treatment.

(15.65)

Click to select the conditions that you want to apply. Specify what you want the rule to do when the conditions are met. In this example, select the Move the item to folder check box. Click the Select Folder button. The Rules and Alerts dialog box appears.

Thus VI is a spin representative of a product of commuting plane rotations. Again, from (15.42), f2a+lf2a = XaZa+1Ya = iZaZ a + l (a = 1, ... , n - 1) f l f 2n = ZI(X I . . . Xn-l)Yn = -iZ 1 Z n(X I .,. X n) By (15.38), (15.66)

V2 =

e{1<ZaZa+l]

e i {1<Ur1r 2n ni:

(15.67)

(15.68)

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FIGURE 1.4 This is known as a triple top, where a new high happens three times, but the price can t get above it. Once the attempts at overcoming this resistance failed, the stock collapsed.

Were it not for the first factor in (15.67), V2 would also be the spin representative of a product of commuting plane rotations. This factor owes its existence to the toroidal boundary condition imposed on the problem (i.e., the condition that 5 n + l == 51 in every row of the lattice). At first sight this condition seems to be an unnecessary and artificial complication, but it actually simplifies our future task. Substituting (15.67) and (15.65) into (15.63) we obtain

[11

e-icf>r2a+lr2a] [

7 9 10 8

e-iornrn-l]

(15.69)

U(l + U) =1 + U,

U(1 - U) = - (1 - U)

(15.70) nf f f (b) U = i l 2 (15.71) 2n (c) U commutes with a product of an even number of fl! and anticommutes with a product of an odd number of fl!' * A simple calculation shows that

earlier at $34 promised themselves that the moment the stock recovered to a break-even level, they would get out. Perhaps most people felt the stock was fully valued at $34. The reasons really don t matter; the fact is that over a six-month period, there was an invisible line drawn on the stock chart through which prices simply could not pass. What happened afterwards is very interesting: far from pushing above the $34 price, the stock instead started collapsing. As Figure 1.5 shows, CHK withered away from $34 per share to about 50 cents, almost a 99% decline. Clearly the stock had worse problems than a triple top, but the important point here is that the market was telling the owners of the stock something, and the triple top was a warning that this was a stock to sell, not keep.

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