Thermodynamic limit for the distribution function of the effective field of random ising models on the linear chain or on the Cayley tree

T. Morita

Physica A: Statistical Mechanics and its Applications, 1980, vol. 103, issue 1, 354-362

Abstract: The integrated probability distribution functions of the effective field νi(h) on the site i satisfy a recurrence formula for the random Ising model on the linear chain or on the Cayley tree. Assuming that the values of the exchange integral are bounded, we prove for the system on the linear chain at an arbitrary temperature and for the system on the Cayley tree at high temperatures, that the inverse function hi(ν) of the function νi(h) converges uniformly to a limiting function h(ν) in the thermodynamic limit. For these systems we see that, when the integral equation for the limiting function ν(h) of νi(h) is solved by iteration, the convergence is uniform for the inverse function h(ν) of ν(h).

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:103:y:1980:i:1:p:354-362

DOI: 10.1016/0378-4371(80)90223-X

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