Thermodynamic lilit in a stronger sense for random systems

The concept of thermodynamic limit in a stronger sense is introduced for random systems. It is then shown that the thermodynamic limit exists in the stronger sense for the one-dimensional random Ising model, under the assumption that the exchange integrals take values within a bounded interval. The corresponding argument for the Ising model on the Cayley tree shows the existence of the thermodynamic limit for the random Ising model on the Bethe lattice (central part of the Cayley tree) at high temperatures.