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