1974/05/07 by A. B. Harris, A B Harris · 12 citations
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.1088/0022-3719/7/9/009
crossref issued 1974/05/07 · crossref published 1974/05/07 · crossref published-print 1974/05/07 · openalex publication_date 1974/05/07 · crossref published-online 2001/02/28 · crossref created 2002/07/26 · crossref deposited 2020/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30 · crossref indexed 2026/07/31
A cumulant expansion is used to calculate the transition temperature of Ising models with random-bond defects. For a concentration, x, of missing interactions in the simple-square Ising model the author finds -T c -1 dT c /dx mod x=0 =1.329 compared with the mean-field value of one. If the interactions are independent random variable with a width delta J/J identical to epsilon , the result is -T c -1 dT c /d epsilon 2 mod epsilon =0 =0.312 compared with the mean-field results of zero. An approximation yields the specific heat in the critical regime as C approximately C 0 /(1+x gamma 2 C 0 ), where gamma is a constant and C 0 is the unperturbed specific heat at a renormalized temperature. Thus, the specific heat divergence is broadened over a temperature interval Delta T, with Delta T/T c approximately x (1 alpha )/, where alpha is the critical exponent for the specific heat, and a maximum value of order x -1 is attained. Heuristic arguments show that this smoothing effect occurs if alpha >0.