  We propose a thermodynamic multi-state spin model in order to describe
equilibrial behavior of a society. Our model is inspired by the Axelrod model
used in social network studies. In the framework of the statistical mechanics
language, we analyze phase transitions of our model, in which the spin
interaction $J$ is interpreted as a mutual communication among individuals
forming a society. The thermal fluctuations introduce a noise $T$ into the
communication, which suppresses long-range correlations. Below a certain phase
transition point $T_t$, large-scale clusters of the individuals, who share a
specific dominant property, are formed. The measure of the cluster sizes is an
order parameter after spontaneous symmetry breaking. By means of the Corner
transfer matrix renormalization group algorithm, we treat our model in the
thermodynamic limit and classify the phase transitions with respect to inherent
degrees of freedom. Each individual is chosen to possess two independent
features $f=2$ and each feature can assume one of $q$ traits (e.g. interests).
Hence, each individual is described by $q^2$ degrees of freedom. A single first
order phase transition is detected in our model if $q>2$, whereas two distinct
continuous phase transitions are found if $q=2$ only. Evaluating the free
energy, order parameters, specific heat, and the entanglement von Neumann
entropy, we classify the phase transitions $T_t(q)$ in detail. The permanent
existence of the ordered phase (the large-scale cluster formation with a
non-zero order parameter) is conjectured below a non-zero transition point
$T_t(q)\approx0.5$ in the asymptotic regime $q\to\infty$.
