RT Journal Article T1 Staircase to higher-order topological phase transitions A1 Cats, P. A1 Quelle, A. A1 Viyuela, O. A1 Martín-Delgado Alcántara, Miguel Ángel A1 Morais Smith, C. AB We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of the pairing interaction, which is parametrized by an algebraic decay with exponent α. Remarkably, in the limit α = 1 the order of the topological transition becomes infinite. We compute the critical exponents for the series of higher-order transitions in exact form and find that they fulfill the hyperscaling relation. We also study the critical behavior at the boundary of the system and discuss potential experimental platforms of magnetic atoms in superconductors. PB American Physical Society SN 2469-9950 YR 2018 FD 2018-03-12 LK https://hdl.handle.net/20.500.14352/12039 UL https://hdl.handle.net/20.500.14352/12039 LA eng NO © 2018 American Physical Society. The work by A.Q. and C.M.S. is part of the D-ITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW). M.A.M.-D. and O.V. acknowledge financial support from the Spanish MINECO Grants No. FIS2012-33152 and No. FIS2015-67411 and the CAM research consortium QUITEMAD+, Grant No. S2013/ICE-2801. The research of M.A.M.-D. has been supported, in part, by the U.S. Army Research Office through Grant No. W911N F-14-1-0103. O.V. thanks Fundación Ramón Areces, Fundación Rafael del Pino and RCC Harvard. NO Ministerio de Economía y Competitividad (MINECO) NO Comunidad de Madrid NO U.S. Army Research Office DS Docta Complutense RD 8 abr 2025