CALCULATION OF PHYSICAL PROPERTIES OF CO-OPERATIVE ASSEMBLIES.
Final technical rept. May 68-Apr 69,
KING'S COLL LONDON (ENGLAND) DEPT OF THEORETICAL PHYSICS
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It is shown that there is a direct correspondence between an exponent representing the high temperature critical behavior of the Ising or Heisenberg model and a corresponding geometrical property of a self avoiding walk. For example the magnetic susceptibility corresponds to the total number of walks, the pair correlation function to the probability distribution of end points, and the gap index to the second virial coefficient of two walks. However, this provides only a first approximation to the exponent of the Ising or Heisenberg model. To proceed to the correct value, one must consider the problem of near neighbor contacts along self avoiding walks and the manner in which they are ordered. A parallel investigation has shown how the transition is effected from a normal random walk to a self avoiding walk and how the dramatic change in properties arises. The equation of state in the critical region in a non-zero magnetic field has been calculated for the speherical model with long range forces and the equation conforms to the expected pattern. An analogous formula has been put forward for the equation satisfied by the pair correlation function. New experimental data on specific heats to compare them with theoretical predictions is analyzed. Author
- Solid State Physics