On the critical behavior of the magnetization in high-dimensional Ising models

1986/08/01 by Michael Aizenman, M. Aizenman, R. Fern�ndez · 1 voice · 5 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.1007/bf01011304

crossref issued 1986/08/01 · crossref published 1986/08/01 · crossref published-print 1986/08/01 · openalex publication_date 1986/08/01 · crossref created 2005/02/05 · crossref deposited 2019/04/27 · openalex created_date 2025/10/10 · crossref indexed 2026/06/06 · openalex updated_date 2026/07/23

Cited by

• Analytic expressions for estimation of the critical properties of inhomogeneous Ising models
• Rigorous Analysis of Discontinuous Phase Transitions via Mean-Field Bounds
• Random subgraphs of finite graphs: I. The scaling window under the triangle condition
• Sociophysics models inspired by the Ising model
• Graphical representations of Ising and Potts models

Discussions

• The Ising model has a continuous phase transition in every dimension $d\geq 2$ (that is, the magnetization vanishes continuously at the critical temperature). This was proved by Aizenman and Fernandez [stackexchange, 4 points]