In an informal way, a number of thoughts on the financial crisis 2008 are presented from a physicist's viewpoint, considering the problem as a nonergodicity transition of a spin-glass type of system. Some tentative suggestions concerning the way out of the crisis are also discussed, concerning Keynesian "deficit spending" methods, tax reductions, and finally the method "ruin and recreate" known from optimization theory. Also the de Almeida-Thouless instability line of spin-glass theory is given a financial interpretation.
Deep Dive into On the Financial Crisis 2008 from a Physicists viewpoint: A Spin-Glass Interpretation.
In an informal way, a number of thoughts on the financial crisis 2008 are presented from a physicist’s viewpoint, considering the problem as a nonergodicity transition of a spin-glass type of system. Some tentative suggestions concerning the way out of the crisis are also discussed, concerning Keynesian “deficit spending” methods, tax reductions, and finally the method “ruin and recreate” known from optimization theory. Also the de Almeida-Thouless instability line of spin-glass theory is given a financial interpretation.
This is an informal communication, not intended for publication. The topic, the financial crisis 2008 and its probable expansion into a serious economic crisis, is closely connected to spin-glass physics, (not only) to the opinion of the author. This is more or less common wisdom of the econophysics community ( [1]). (If you want to comment on some issue, please send mail).
Furthermore, the degrees of freedom of the system, which may be represented by a twodimensional graph, are, in a strong simplification, replaced by binary (i.e., ‘Ising’) degrees of freedom, s i , where the signs, ±1, may correspond to gains and losses, respectively, of the individual companies competing for profit, which are represented by the vertices i of the graph and interact with each other in a global market.
These interactions are frustrated -a notion known from spin-glass theory, e.g. around a closed loop with an odd number of edges, taking the products (‘Wilson loop products’) of an odd number of the Ising variables, the interactions -whatever they may be -will lead to a positive outcome at the end, if the loop product is taken in one direction, and a negative outcome, if it is in the opposite direction. (The frustration or complexity of the system will become important below.)
This possibility of inherent “frustration” in the loop of simultaneous cooperation and competition, [2], (a certain quenched correlation of the system, leading to essentially unavoidable and equally probable gains and losses, where the probability of a loss in a “betting situation” seems to have sometimes been forgotten by the global “players”, or shifted to future generations), is fixed by the interactions on the graph, which is typical for a spin-glass system, assuming that the graph itself is disordered, with fixed random positions and interactions (“quenching”).
Here is the place, where the interest rate, r, of the central bank of the involved currency, comes into play. Since very low values of r enhance the tendency of the investment banks to invent new “structured financial products”, whatsoever, an enhancement(!) of the interest rate should also be considered as a means to reduce the complexity of the financial market, not only as a means to reduce the danger of inflation. Of course, the primary effect of a change of r is in conflict with this consideration: primarily, at low values of r everyone gets loans (e.g., for houses), which then become too expensive, if r is increasing again.
One should also consider that one is not dealing with a closed system, but rather a system with two “sinks”, the Iraque, and Afghanistan.
“Whatever the interactions may be”: this is a crucial text item. Typically, since there are many “groups” (N ≫ 1), the interactions of the system may roughly correspond to a seemingly rather special spherical spin glass, a “p-spin-glass”, i.e. with p interacting spins, where p ≫ 1 (many companies, p, form an interacting group) and where the spherical condition
The following remarks are obvious:
The interaction is described by a global optimization function, corresponding physically to the Hamiltonian of the system, and is not essential, in contrast to the degrees of freedom of the system and some relevant macroscopic variables, e.g. the specific volume or specific size v of a company or group of cooperating companies. In an ideal situation (remember the ideal gas) one thinks ‘The larger the better’, because of the synergies, but the reality may be different: recently one has apparently come to the opposite conclusion that ‘As small as possible’ is more beautiful, because in this way the costs seem to be reduced more effectively (unfortunately, to say it mildly, in both cases the unemployment is enhanced.) This change of paradigm -the analogon is a change of slope of the saturation pressure p(v) -may be considered as a warning signal for criticality.
Another essential physical parameter, the temperature, seems to correspond to the economic activity: enhancing (or reducing) the temperature, respectively, is perhaps analogous to turning up (or slowing down) the economic activity (the analogy is more visible in the German language: “Temperatur” versus “Konjunktur”). Finally, the physical variable p (pressure) may be translated economically into a “reciprocal specific wealth” or “individual economic pressure”, an intensive quantity, in constrast to the size parameter V , which is extensive. (v = V N is the specific company size, or specific group size, where N is the number of companies or groups of cooperating companies).
Furthermore, physically there are two “fluid” phases of a system, a vapor phase, which is a wealthy phase in our economical interpretation, and a liquid (or poor) phase, respectively.
Here the well-known Van der Waals theory (see e.g. [3]) of the vapor ⇔ liquid transition is set into an economical analogy between economic phases with two different degrees of wealth. Physically one has a stable and a metasta
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