2006/10/31 by Yan V. Fyodorov, H. -J. Sommers, H.-J. Sommers · 4 citations
Materials Science · Mathematics · Physics and Astronomy · #Ansatz #Gaussian #Hamiltonian (control theory) #Material Dynamics and Properties #Mathematics #Partition function (quantum field theory) #Physics #Quantum mechanics #Rotational symmetry #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamic limit #cond-mat.dis-nn
paper · pdf · doi:10.1016/j.nuclphysb.2006.11.029
published as Nuclear Physics B, v. 764 [FS], 128-167 (2007) · 46 pages, 4 figures; This version corrects a few more typos discovered in the published version
openalex publication_date 2006/12/21 · arxiv created 2007/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate thermodynamics of a single classical particle placed in a spherical box of a finite radius R and subject to a superposition of a N-dimensional Gaussian random potential and the parabolic potential with the curvature μ>0. Earlier solutions of R→ ∞ version of this model were based on combining the replica trick with the Gaussian Variational Ansatz (GVA) for free energy, and revealed a possibility of a glassy phase at low temperatures. For a general R, we show how to utilize instead the underlying rotational symmetry of the replicated partition function and to arrive to a compact expression for the free energy in the limit N→ ∞ directly, without any need for intermediate variational approximations. This method reveals striking similarity with the much-studied spherical model of spin glasses. Depending on the value of R and the three types of disorder - short-ranged, long-ranged, and logarithmic - the phase diagram of the system in the (μ,T) plane undergoes considerable modifications. In the limit of infinite confinement radius our analysis confirms all previous results obtained by GVA.