Multiscaling at ferromagnetic-spin glass transition point of Random Energy Model and complexity

2000/04/25 by David B. Saakian, D. B. Saakian, Saakian, D. B.
Computer Science · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0004406

9 pages, latex

arxiv created 2000/04/25 · openalex publication_date 2000/04/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We calculate moments of free energy's finite size correction for the transition point between ferromagnetic and spin glass phases. We find, that those moments scale with the number of spins with different critical indices, characteristic for the multiscaling. This critical point corresponds to threshold of errorless coding for a gaussian noisy channel. We are give the definition of statistical complexity using this free energy approach.

Related

• Complexity as the driving force for dynamical glassy transitions
• Critical behavior of random spin systems
• TAP free energy, spin glasses, and variational inference
• Finite size corrections on the boundary between the spin-glass and the ferromagnetic phases of Derrida's model
• Possibly Exact Solution for the Multicritical Point of Finite-Dimensional Spin Glasses