title: Finite size induces crossover temperature in growing spin chains.
abstract: We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.
authors.affiliation: Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
authors.forename: Julian
authors.initials: J
authors.lastname: Sienkiewicz
authors.affiliation: Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Suchecki
authors.affiliation: Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
authors.forename: Janusz A
authors.initials: JA
authors.lastname: Hołyst