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

Unconventional superconductivity and an ambient-pressure magnetic quantum critical point in single-crystal LaNiC2_2

Superconductivity in noncentrosymmetric LaNiC$_2$ is expected to be induced by electron--phonon interactions due to its lack of magnetic instabilities. The non-Bardeen-Cooper-Schrieffer (BCS) behaviors found in this material call into question the long-standing idea that relates unconventional superconductivity with magnetic interactions. Here we report magnetic penetration-depth measurements in a high-purity single crystal of LaNiC$_2$ at pressures up to 2.5 GPa and temperatures down to 0.04 K. At ambient pressure and below 0.5$T_c$ the penetration depth goes as $T^4$ for the in-plane and $T^2$ for the out-of-plane component, firmly implying the existence of point nodes in the energy gap and the unconventional character of this superconductor. The present study also provides first evidence of magnetism in LaNiC$_2$ by unraveling a pressure-induced antiferromagnetic phase inside the superconducting state at temperatures below 0.5 K, with a quantum critical point around ambient pressure. The results presented here maintain a solid base for the notion that unconventional superconductivity only arises near magnetic order or fluctuations.Comment: 12 pages, 4 figure

High-resolution magnetic penetration depth and inhomogeneities in locally noncentrosymmetric SrPtAs

We present a magnetic-penetration-depth study on polycrystalline and granular samples of SrPtAs, a pnictide superconductor with a hexagonal structure containing PtAs layers that individually break inversion symmetry (local noncentrosymmetry). Compact samples show a clear-cut s-wave-type BCS behavior, which we consider to be the intrinsic penetration depth of SrPtAs. Granular samples display a sample-dependent second diamagnetic drop, attributed to the intergrain coupling. Our experimental results point to a nodeless isotropic superconducting energy gap in SrPtAs, which puts strong constraints on the driven mechanism for superconductivity and the order parameter symmetry of this compound

Evidence of s-wave superconductivity in ternary intermetallic La3Pd4Si4

We measured the temperature dependence of the magnetic penetration depth of La3Pd4Si4 down to 0.02 Tc. We observe a temperature-independent behaviour below 0.25 Tc, which is firm evidence for a nodeless superconducting gap in this material. The data display a very small anomaly around 1 K which we attribute to the possible presence of a superconducting impurity phase. The superfluid density is well described by a two-phase model, considering La3Pd4Si4 and the impurity phase. The present analysis suggests that the superconducting energy gap of La3Pd4Si4 is isotropic, as expected for conventional BCS superconductors

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

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

Emergent Nodal Excitations due to the Coexistence of Superconductivity and Antiferromagnetism: Cases with and without Inversion Symmetry

We argue the emergence of nodal excitations due to the coupling with static antiferromagnetic order in fully-gapped superconducting states in both cases with and without inversion symmetry. This line node structure is not accompanied with the sign change of the superconducting gap, in contrast to usual unconventional Cooper pairs with higher angular momenta. In the case without inversion symmetry, the stability of the nodal excitations crucially depends on the direction of the antiferromagnetic staggered magnetic moment. A possible realization of this phenomenon in CePt$_3$Si is discussed.Comment: 4 pages, 7 figure

AC/DC Susceptibility of the Heavy-Fermion Superconductor CePt3Si under Pressure

We have investigated the pressure dependence of ac and dc susceptibilities of the heavy-fermion superconductor CePt3Si (Tc= 0.75 K) that coexists with antiferromagnetism (TN = 2.2 K). As hydrostatic pressure is increased, Tc first decreases rapidly, then rather slowly near the critical pressure Pc = 0.6 GPa and shows a stronger decrease again at higher pressures, where Pc is the pressure at which TN becomes zero. A transition width and a difference in the two transition temperatures defined in the form of structures in the out-of-phase component of ac susceptibilities also become small near Pc, indicating that a double transition observed in CePt3Si is caused by some inhomogeneous property in the sample that leads to a spatial variation of local pressure. A sudden increase in the Meissner fraction above Pc suggests the influence of antiferromagnetism on superconductivity.Comment: 4 pages with 5 figures. This paper will be published in J. Phys. Soc. Jp

A Possible Phase Transition in beta-pyrochlore Compounds

We investigate a lattice of interacting anharmonic oscillators by using a mean field theory and exact diagonalization. We construct an effective five-state hopping model with intersite repulsions as a model for beta-pyrochlore AOs_2O_6(A=K, Rb or Cs). We obtain the first order phase transition line from large to small oscillation amplitude phases as temperature decreases. We also discuss the possibility of a phase with local electric polarizations. Our theory can explain the origin of the mysterious first order transition in KOs_2O_6.Comment: 4 pages, 4 figures, submitted to J. Phys. Soc. Jp