Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model

We investigate the phase diagram of a spin-$1/2$ Ising model on a cubic lattice, with competing interactions between nearest and next-nearest neighbors along an axial direction, and fully connected spins on the sites of each perpendicular layer. The problem is formulated in terms of a set of noninteracting Ising chains in a position-dependent field. At low temperatures, as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising (ANNNI) model, there are many distinct spatially commensurate phases that spring from a multiphase point of infinitely degenerate ground states. As temperature increases, we confirm the existence of a branching mechanism associated with the onset of higher-order commensurate phases. We check that the ferromagnetic phase undergoes a first-order transition to the modulated phases. Depending on a parameter of competition, the wave number of the striped patterns locks in rational values, giving rise to a devil's staircase. We numerically calculate the Hausdorff dimension $D_{0}$ associated with these fractal structures, and show that $D_{0}$ increases with temperature but seems to reach a limiting value smaller than $D_{0}=1$.Comment: 17 pages, 6 figure

Three routes for sustainable consumer behaviours

As societies become aware of environmental issues, a large portion of consumers are adopting more sustainable lifestyles and refraining from buying certain products (EIB, 2021), with environmental motives predicted to be the top choice criteria for as much as 55% of consumers in the next five years (betterRetailing.com, 2021). An area of particular dispute in literature is between adopting self-oriented (e.g., related with improving our social/self-identity) or altruistic (e.g., environmental-related) motives for explaining sustainable consumer behaviors (SCBs). In particular, social norms (SN) and environmental concerns (EC) are the two most frequently assessed predictors of SCBs according to our exploratory literature review, yet with contradictory findings. The aim of this study is to examine whether consumers, confronted with choosing between environmentally sustainable and non-sustainable products, show higher consideration for social self-enhancement, or environmental motives, and observe to what extent does that influence differs across green categories. We address the following research questions: RQ1: Which green product categories are spontaneously mentioned by consumers? RQ2: To what extent did social and/or environmental factors influenced their choices? RQ3: What other motivations and barriers may affect SCBs?info:eu-repo/semantics/publishedVersio