.net code 39 reader

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One of the most interesting phenomena in the physics of the solid state is ferromagnetism. In some metals, e.g., Fe and Ni, a finite fraction of the spins of the atoms brcomes spontaneously polarized in the same direction, giving rise to a macroscopic magnetic field. This happens, however, only when the temperature is lower than a characteristic temperature known as the Curie temperature. Above the Curie temperature the spins are oriented at random, producing no net magnetic field. As the Curie temperature is approached from both sides the specific heat of the metal approaches infinity. The Ising model is a crude attempt to simulate the structure of a physical ferromagnetic substance. * Its main virtue lies in the fact that a two-dimensional Ising model yields to an exact treatment in statistical mechanics. It is the only nontrivial example of a phase transition that can be worked out with mathematical rigor. In the Ising mode1 t the system considered is an array of N fixed points called lattice sites that form an n-dimensional periodic lattice (n = 1,2,3). The geometrical structure of the lattice may (for example) be cubic or hexagonal. Associated with each lattice site is a spin variable Si (i = 1, ... , N) which is a number that is either + 1 or -1. There are no other variables. If Si = + 1, the ith site is said to have spin up, and if Si = -1, it is said to have spin down. A given set of numbers {s,} specifies a configuration of the whole system. The energy of the system in the configuration specified by {Si} is defined to be

EJ{Si}

"More accurately, the Ising model simulates a "domain" in a ferromagnetic substance. A discussion of the physical properties and the atomic structure of ferromagnets (and antiferromagnets) is beyond the scope of the present discussion. For information in these aspects consult a book on solid-state physics. t E. Ising. Z. Phys. 31, 253 (1925).

where the subscript I stands for Ising and the symbol (ij) denotes a nearestneighbor pair of spins. There is no distinction between (ij) and (ji). Thus the sum over (ij) contains yN/2 terms, where y is the number of nearest neighborof any given site. For example, 4 (two-dimensional square lattice)

6 (three-dimensional simple cubic lattice) 8 (three-dimensional body-centered cubic lattice)

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The interaction energy . i) and the external magnetic field H are given constants The geometry of the lattice enters the problem through y and . i)' For simplicit\ we specialize the model to the case of isotropic interactions, so that all . i) are equal to a given number (. Thus the energy will be taken as

EJ{Si}

The result is shown in Figure 6.17, with three moving averages overlaid on the price chart. A legend of the studies appears just beneath the data line, showing each of the studies followed by (1) its current numeric value, based on where you are pointing on the chart; and (2) its last, most recent value from the chart, since the Show Last Value checkbox was checked on the technical studies editor. Now that you understand how to combine technical studies, you can use the time-saving Study Sets feature.

L SiS) -

(14.1

The case . > 0 corresponds to ferromagnetism and the case . < 0 to antiferromagnetism. We consider only the case . > O. The partition function is

(14.21

where each Si ranges independently over the values 1. Hence there are 2 N terms in the summation. The thermodynamic functions are obtained in the usual manner from the Helmholtz free energy:

AJ(H,T)

-kTlogQJ(H,T)

7 4 5 6

As you become more expert with various studies, you will nd certain ones that you especially like to use. You will also nd that some combinations of these studies work well together, since they can be used to help you weigh your trading decisions and, in a way, vote on whether you are going to buy a stock or not. You may even nd yourself so adept with some indicators that you adjust their parameters (certainly those involving appearance) to your liking.

(14.31

UJ(H, CJ(H,

T) T)

aaT (:;)

(internal energy) (heat capacity)

(14.41 (14.5 )

(magnetization)

(14.6)

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