Application of physical methods in economical analysis often proves to be highly fruitful (see, for example, book [1]). The analysis we carried out in the previous work [2] revealed isomorphism of dynamical networks of the financial market (either stock or currency one) and crystalline solid state, which allows to efficiently study financial markets with the help of already worked out and applied methods of solid state physics.
One of basic fundamental theoretical models of solid state physics is t - J model [3], representing a particular case of a well-known Hubbard model [4]. t - J model is characterized with two physical parameters, each being able to have economical interpretation: 1) exchange energy J - market liquidity (which can be quantitatively determined as, for instance, volume of tenders in the unit of time); 2) electron concentration n - market price of goods (here, shares and currency). In the frame of t - J model there can be described three types magnetically ordered phases (characterized with various value of magnetization m ) - paramagnetism ( m = 0 ) , saturated ferromagnetism ( m = n ) and non-saturated ferromagnetism ( 0 < m < n ). Relative numbers of sellers and buyers in the market (i.e. their total shares) can be compared correspondingly to relative magnetization m/n and its conjugated value 1 - m/n . Non-saturated ferromagnetism then would correspond with a stable market (a market with both sellers and buyers), while saturated ferromagnetism and paramagnetism - with two opposite types of a non-stable market: "not buying" market (a market with sellers, but with no buyers) and "not selling" market (a market with buyers, but no sellers), correspondingly.
An economical interpretation of physical concepts we have made allows to consider magnetic phase diagram of t - J model [5] constructed on the plane of J and n parameters as a diagram of the financial market state. Besides, with the help of the connection of magnetization with electron concentration and exchange energy, we found in [5], we received functional dependence of relative numbers of sellers and buyers in the market on the market price of goods and market liquidity. It can be seen, that at any fixed liquidity the received dependence in qualitative sense completely corresponds with the revealed in the classical work [6] dependence of supply and demand volumes on the market price of the goods. The revealed correspondence allows to calculate equilibrium price (answering the coincidence of supply and demand volumes) [6] at any market liquidity under equal numbers of sellers and buyers. The very procedure allows to construct a diagram of dependence of equilibrium price on market liquidity, representing a monotonously increasing curve.
The work has been carried out with partial support of RGNF Grant ¹ 01-02-00114a.
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(Walras L., Elements of Pure Economics, Irwin: W. Jaffe, 1954.)