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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 $qtoinfty$.
We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytica
We study a nonequilibrium model with up-down symmetry and a noise parameter $q$ known as majority-vote model of M.J. Oliveira 1992 with heterogeneous agents on square lattice. By Monte Carlo simulations and finite-size scaling relations the critical
We investigate the Hubbard model on a two-dimensional square lattice by the perturbation expansion to the fourth order in the on-site Coulomb repulsion U. Numerically calculating all diagrams up to the fourth order in self-energy, we examine the conv
We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show th
In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by Watari and Tsutahara [Phys Rev E textbf{67},036306