2004/07/12 by Cécile Monthus, Cecile Monthus, Pierre Le Doussal
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Cumulant #Degenerate energy levels #Distribution (mathematics) #Ising model #Material Dynamics and Properties #Mathematical analysis #Mathematics #Observable #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #Statistics #Theoretical and Computational Physics #Thermal fluctuations #cond-mat.dis-nn #math.PR
paper · pdf · doi:10.1140/epjb/e2004-00351-2
published as Eur. Phys. J. B 41, 535 (2004) · 19 pages, 4 figures
arxiv created 2004/07/12 · openalex publication_date 2004/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The thermal fluctuations that exist at very low temperature in disordered systems are often attributed to the existence of some two-level excitations. In this paper, we revisit this question via the explicit studies of the following 1D models (i) a particle in 1D random potentials (ii) the random field Ising chain with continuous disorder distribution. In both cases, we define precisely the `two-level' excitations and their statistical properties, and we show that their contributions to various observables are in full agreement at low temperature with the the rigorous results obtained independently. The statistical properties of these two-level excitations moreover yield simple identities at order T in temperature for some generating functions of thermal cumulants. For the random-field Ising chain, in the regime where the Imry-Ma length is large, we obtain that the specific heat is dominated by small non-universal excitations, that depend on the details of the disorder distribution, whereas the magnetic susceptibility and the Edwards-Anderson order parameter are dominated by universal large excitations, whose statistical properties only depend on the variance of the initial disorder via the Imry-Ma length.