2021/02/28 by C. D. Rodríguez-Camargo, Eduardo Mojica‐Nava, E. A. Mojica-Nava +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Geometry #Mathematical analysis #Mathematical optimization #Mathematics #Metastability #Partition function (quantum field theory) #Physics #Quantum mechanics #Saddle #Saddle point #Spin glass #Statistical Mechanics and Entropy #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.104.034102
published as Phys. Rev. E 104, 034102 (2021) · 14 pages, 8 figures
arxiv created 2021/07/05 · openalex publication_date 2021/09/02 · arxiv updated 2021/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss the Sherrington-Kirkpatrick mean-field version of a spin glass within the distributional zeta function method (DZFM). In the DZFM, since the dominant contribution to the average free energy is written as a series of moments of the partition function of the model, the spin-glass multivalley structure is obtained. Also, an exact expression for the saddle points corresponding to each valley and a global critical temperature showing the existence of many stables or at least metastable equilibrium states is presented. Near the critical point, we obtain analytical expressions of the order parameters that are in agreement with phenomenological results. We evaluate the linear and nonlinear susceptibility and we find the expected singular behavior at the spin-glass critical temperature. Furthermore, we obtain a positive definite expression for the entropy and we show that ground-state entropy tends to zero as the temperature goes to zero. We show that our solution is stable for each term in the expansion. Finally, we analyze the behavior of the overlap distribution, where we find a general expression for each moment of the partition function.