Statistical system based on p-adic numbers

We propose statistical systems based on p -adic numbers. In the systems, Hamiltonian is a standard real number which given by map from Therefore we can introduce temperature as and calculate thermodynamical quantities like free energy, entropy, specific heat, etc. Although consider very simple system, corresponds to particle moving in one dimensional space, find that there appear behaviors phase transition system. Usually order occurs, need system with an infinite of degrees freedom but where dynamical variable number, even if degree unity, might occur transition.