A Fully Magnetizing Phase Transition

1998/11/20 by Pierluigi Contucci, Peter Kleban, Andreas Knauf · 7 citations
Mathematics · Physics and Astronomy · #Farey sequence #Magnetization #Markov Chains and Monte Carlo Methods #Micromagnetics #Phase (matter) #Phase transition #Spin (aerodynamics) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Zero (linguistics) #Zero temperature #cond-mat #math-ph #math.MP #math.NT #msc:82B26

paper · pdf · doi:10.1023/a:1004607107241

published in Journal of Statistical Physics 97(3-4), 523-539 (Springer Science+Business Media) · 19 pages

arxiv created 1998/11/20 · openalex publication_date 1999/11/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We analyze the Farey spin chain, a one dimensional spin system with effective interaction decaying like the squared inverse distance. Using a polymer model technique, we show that when the temperature is decreased below the (single) critical temperature T_c=1/2, the magnetization jumps from zero to one.

Citations

• An introduction to chromatic polynomials
• Existence of a phase-transition in a one-dimensional Ising ferromagnet