2010/04/30 by Takashi Mori
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boundary value problem #Condensed matter physics #Field (mathematics) #Field theory (psychology) #Lattice (music) #Magnetic field #Magnetization #Materials science #Mathematical physics #Mathematics #Mean field theory #Metastability #Periodic boundary conditions #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Range (aeronautics) #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.82.060103
published as Phys. Rev. E 82, 060103(R) (2010) · 4 pages, 5 figures; clarifications and discussion about boundary effects is added; the title is changed
openalex publication_date 2010/12/21 · arxiv created 2013/06/20 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Relationships between general long-range interacting classical systems on a lattice and the corresponding mean-field models (infinitely long-range interacting models) are investigated. We study systems in arbitrary dimension d for periodic boundary conditions and focus on the free energy for fixed value of the total magnetization. As a result, it is shown that the equilibrium free energy of the long-range interacting systems are exactly the same as that of the corresponding mean-field models (exactness of the mean-field theory). Moreover, the mean-field metastable states can be also preserved in general long-range interacting systems. It is found that in the case that the magnetization is conserved, the mean-field theory does not give correct property in some parameter region.