A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

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 analytically calculate thermodynamic and critical properties for a 1D system and show that an order-disorder phase transition only occurs at T = 0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.Comment: 19 pages, 5 figure

Cluster size entropy in the Axelrod model of social influence: small-world networks and mass media

We study the Axelrod's cultural adaptation model using the concept of cluster size entropy, $S_{c}$ that gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is unambiguously given by the maximum of the $S_{c}(q)$ distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first- or second-order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait $q_c$ and the number $F$ of cultural features in regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a new partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a new $q-B$ phase diagram for the Axelrod model in regular networks.Comment: 21 pages, 7 figure

Superconductivity and normal state properties of non-centrosymmetric CePt₃Si: a status report

Ternary CePt₃Si crystallizes in the tetragonal P4mm structure which lacks a center of inversion. Antiferromagnetic order sets in at TN≈22 . K followed by superconductivity (SC) below Tc≈ 0.75 K. Large values of H'c2≈-8.5 T/K and Hc2(0)≈5T were derived, referring to Cooper pairs formed out of heavy quasiparticles. The mass enhancement originates from Kondo interactions with a characteristic temperature TK≈ 8 K. CePt₃Si follows the general features of correlated electron systems and can be arranged within the Kadowaki–Woods plot next to the unconventional SC UPt₃. NMR and mSR results show that both magnetic order and SC coexist on a microscopic scale without having spatial segregation of both phenomena. The absence of an inversion symmetry gives rise to a lifting of the degeneracy of electronic bands by spin-orbit coupling. As a consequence, the SC order parameter may have uncommon features as indicated from a very unique NMR relaxation rate 1/T₁ and a linear temperature dependence of the penetration depth λ

Unusual behaviours and Impurity Effects in the Noncentrosymmetric Superconductor CePt3Si

We report a study in which the effect of defects/impurities, growth process, off-stoichiometry, and presence of impurity phases on the superconducting properties of noncentrosymmetric CePt3Si is analysed by means of the temperature dependence of the magnetic penetration depth. We found that the linear low-temperature response of the penetration depth -indicative of line nodes in this material- is robust regarding sample quality, in contrast to what is observed in unconventional centrosymmetric superconductors with line nodes. We discuss evidence that the broadness of the superconducting transition may be intrinsic, though not implying the existence of a second superconducting transition. The superconducting transition temperature systematically occurs around 0.75 K in our measurements, in agreement with resistivity and ac magnetic susceptibility data but in conflict with specific heat, thermal conductivity and NMR data in which Tc is about 0.5 K. Random defects do not change the linear low-temperature dependence of the penetration depth in the heavy-fermion CePt3Si with line nodes, as they do in unconventional centrosymmetric superconductors with line nodes.Comment: To appear in New Journal of Physic

Non-Locality and Strong Coupling in the Heavy Fermion Superconductor CeCoIn5_{5}: A Penetration Depth Study

We report measurements of the magnetic penetration depth $\lambda$ in single crystals of CeCoIn$_{5}$ down to $\sim$0.14 K using a tunnel-diode based, self-inductive technique at 28 MHz. While the in-plane penetration depth tends to follow a power law, $\lambda_{//} \sim {\it T}^{3/2}$, the data are better described as a crossover between linear ({\it T} $\gg$ ${\it T}^\ast$) and quadratic ({\it T} $\ll {\it T}^\ast$) behavior, with ${\it T}^\ast$ the crossover temperature in the strong-coupling limit. The {\it c}-axis penetration depth $\lambda_{\perp}$ is linear in {\it T}, providing evidence that CeCoIn$_{5}$ is a {\it d}-wave superconductor with line nodes along the {\it c}-axis. The different temperature dependences of $\lambda_{//}$ and $\lambda_{\perp}$ rule out impurity effects as the source of ${\it T}^{\ast}$.Comment: 4 pages, 3 figure