1998/06/16 by Kuelske, Christof, Christof Kuelske · 1 citation
Mathematics · Physics and Astronomy · #Condensed matter physics #Ferromagnetism #Field (mathematics) #Mathematics #Physics #Pure mathematics #Quantum chaos and dynamical systems #Random field #Spectral Theory in Mathematical Physics #Spin (aerodynamics) #Statistical physics #Statistics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:82B26 #msc:82B28 #msc:82B44
paper · pdf · doi:10.1142/s0129055x99000404
46 pages
arxiv created 1998/06/16 · openalex publication_date 1998/06/16 · arxiv updated 2015/06/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
We investigate the Gibbs-measures of ferromagnetically coupled continuous spins in double-well potentials subjected to a random field (our specific example being the φ4 theory), showing ferromagnetic ordering in d≥ 3 dimensions for weak disorder and large energy barriers. We map the random continuous spin distributions to distributions for an Ising-spin system by means of a single-site coarse-graining method described by local transition kernels. We derive a contour- representation for them with notably positive contour activities and prove their Gibbsianness. This representation is shown to allow for application of the discrete-spin renormalization group developed by Bricmont/Kupiainen implying the result in d≥ 3.