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We suppose that, in the limit t -+ 0, any thermodynamic quantity can be decomposed into a "regular" part, which remains finite (but not necessary continuous), plus a "singular" part that may be divergent, or have divergent derivatives. The singular part is assumed to be proportional to some power of t, generally fractional. The first four critical exponents are defined as follows: Heat capacity: Order parameter: Susceptibility: Equation of state (t = 0):

(16.21) (16.22) (16.23) (16.24)

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Here - means" has a singular part proportional to." Since the first three relations all refer to a phase transition, it is understood that H = O. The last one, on the other hand, specifically refers to the case H =1= O.

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We should keep in mind that these behaviors refer only to the singular part. For example, a = 0 means that the heat capacity has no singular part; but it may still have a finite discontinuity at 1 = O. The definitions above implicitly assume that the singularities are of the same type, whether we approach the critical point from above or from below. This has been borne out both theoretically and experimentally, except for M, which is identically zero above the critical point by definition. Thus obviously (16.22) makes sense only for 1 < O. We shall not bother to make this qualification every time. The last two in the Greek alphabet soup of exponents concern the correlation function, which we shall assume to have the Ornstein-Zernike form

/-.0

(16.25)

1. Choose the Fibonacci fan tool from the toolbar. 2. Draw a line from the low on February 12, 2003 at 40.62 cents all the

- 111-"

(16.26)

d - 2

(16.27)

The significance of the critical exponents lie in their universality. As experiments have shown, widely different systems, with critical temperatures differing by orders of Ir..agnitudes, approximately share the same critical exponents. Their definitions have been dictated by experimental convenience. Some other linear c:.nmbinations of them have more fundamental significance, as we shall see later. Only two of the six critical exponents defined in the preceding discussion are independent, because of the following "scaling laws": Fisher: Rushbrooke: Widom: Josephson:

Table button, 62 table fields, 157, 160, 161 table of contents, 70 71 table records, 167 table views, 158 159 tables adding to queries, 179 records, 166 167 to slides, 141 creating, 156 157 deleting, 157 inserting, 62 63 relationships, 180 styles, 63 tabs, 8 9, 50 51 Tasks component (Outlook), 194 195

= v(2 -

(16.28) (16.29) (16.30) (16.31)

y = /3( 8 - 1)

way up to the extreme high of $52.72 on July 6, 2006 (an amazing 130fold increase in price in just over three years). 3. Release the mouse, thus displaying the Fibonacci fans. The three arrows on the chart indicate where the price reversed off the highest fan line. This is a good con rmation of the Fibonacci-friendly nature of this stock with respect to these fan lines. Now suppose you had sold this stock short in July as it started to ease. As sensational a run-up as this stock has had, it s obviously very strong and has no clear areas of support. The question is: when do you take pro ts On August 7, 2006, HANS started to plunge on record volume. If you

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