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We propose a thermodynamic multi-state spin model in order to describeequilibrial behavior of a society. Our model is inspired by the Axelrod modelused in social network studies. In the framework of the statistical mechanicslanguage, we analyze phase transitions of our model, in which the spininteraction $J$ is interpreted as a mutual communication among individualsforming a society. The thermal fluctuations introduce a noise $T$ into thecommunication, which suppresses long-range correlations. Below a certain phasetransition point $T_t$, large-scale clusters of the individuals, who share aspecific dominant property, are formed. The measure of the cluster sizes is anorder parameter after spontaneous symmetry breaking. By means of the Cornertransfer matrix renormalization group algorithm, we treat our model in thethermodynamic limit and classify the phase transitions with respect to inherentdegrees of freedom. Each individual is chosen to possess two independentfeatures $f=2$ 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 firstorder phase transition is detected in our model if $q>2$, whereas two distinctcontinuous phase transitions are found if $q=2$ only. Evaluating the freeenergy, order parameters, specific heat, and the entanglement von Neumannentropy, we classify the phase transitions $T_t(q)$ in detail. The permanentexistence of the ordered phase (the large-scale cluster formation with anon-zero order parameter) is conjectured below a non-zero transition point$T_t(q)\approx0.5$ in the asymptotic regime $q\to\infty$.

Thermodynamic model of social influence on two-dimensional square lattice: Case for two features