2020/05/31 by A. A. Berzin, A. I. Morosov, A. S. Sigov
Mathematics · Physics and Astronomy · #Critical dimension #Curse of dimensionality #Dimension (graph theory) #Ising model #Opinion Dynamics and Social Influence #Phase (matter) #Phase diagram #Phase transition #Random field #Space (punctuation) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1134/s1063783421010042
openalex created_date 2020/05/21 · arxiv created 2020/07/05 · openalex publication_date 2021/01/01 · arxiv updated 2021/02/24 · openalex updated_date 2026/08/05
Abstract The “temperature–defect concentration” phase diagram of quasi-one-dimensional Ising models with defects of the “random local field” type is studied. The competition of the tendency to the formation of a long-range order due to a weak interaction between one-dimensional spin chains and the tendency to the formation of the Imry–Ma phase in which the order parameter follows fluctuations of a random field induced by defects is studied too. The formation of the Imry–Ma phase is shown to be possible in the situation as the space dimension is higher than the lower critical dimension. The problem of the existence a long-range order in the Ising model with random fields is considered in a space with critical dimension di = 2.