The Ising Model

The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states. The spins are arranged in a lattice or graph, and each spin interacts at most with its nearest neighbors. The goal is to find phase changes in the Ising model, as a simplified model of phase changes in real substances.

In 2000 while working on the Murphy’s Price - Volume - Open Interest I started scribbling arrows in a 3 by 3 grid writing about how Price - Volume - Open Interest (PVO) should define trends. The PVO model looked like an Ising model.



Today I will try to explain the 10 year old analogy. In an antiferromagnet there is a tendency for the intrinsic magnetic moments of neighboring valence electrons to point in opposite directions. When all atoms are arranged in a substance so that each neighbor is ‘anti-aligned’, the substance is antiferromagnetic. Antiferromagnets have a zero net magnetic moment, meaning no field is produced by them. Antiferromagnetism can be considered like a neutral market as anti aligned spins (Fig. 1) are similar to non confirmations. Many non confirmations also mean undecided market.

From a PVO perspective, it could be a stock with a positive spin and another with a negative spin causing the aggregate market to be neutral.With the passage of time the neutral situation leads to a topping or bottoming situation, in other words a market bias, spin, direction, Ferromagenetism. A topping, where a market reverses direction sees the price pointing lower, volume leading higher and drop in open interest position (as longs square off – Fig 3). On the other hand a bottoming market ready for reversal is when the prices point up, volumes are still lackluster and negative, but open interest starts to build up new long positions (accumulation – Fig 2). This confirmation among stocks finally gives a negative and positive bias to the market. This is how stock markets could have a physics parallel in the Ising model spins. The Ising model could also validate the weight of evidence approach in technical analysis.

This article was written for ATMA.


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