2008/04/08 by Nuno Crokidakis, N. Crokidakis, Fernando Nobre +1 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.77.041124
published as Phys. Rev. E 77, 041124 (2008) · 23 pages, 8 figures, accept for publication in Phys. Rev. E
arxiv created 2008/04/08 · openalex publication_date 2008/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered, respectively, at +H0 and -H0, presenting the same width sigma . It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well-known limits, namely, the single Gaussian distribution (sigma>>H0) and the bimodal one (sigma=0) . The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution. Critical frontiers exhibiting tricritical points occur for different values of sigma , with the possibility of two tricritical points along the same critical frontier. To our knowledge, it is the first time that such a behavior is verified for a spin-glass model in the presence of a continuous-distribution random field, which represents a typical situation of a real system. The stability of the replica-symmetric solution is analyzed, and the usual Almeida-Thouless instability is verified for low temperatures. It is verified that the higher-temperature tricritical point always appears in the region of stability of the replica-symmetric solution; a condition involving the parameters H0 and sigma , for the occurrence of this tricritical point only, is obtained analytically. Some of our results are discussed in view of experimental measurements available in the literature.