2004/04/10 by J. Ricardo de Sousa, de Sousa, J. Ricardo, Beatriz Boechat +7
Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0404251
12 pages, 2 figures; larger version is provided, which will be published in Phs. Rev. E
openalex publication_date 2004/04/10 · arxiv created 2004/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the anisotropic Heisenberg spin-glass model in a three-dimensional hierarchical lattice (designed to approximate the cubic lattice), within a real-space renormalization-group approach. Two different initial probability distributions for the exchange interaction (Jij), Gaussian and uniform, are used, with zero mean and width J. The (kT/J) × Δ0 phase diagram is obtained, where T is the temperature, Δ0 is the first moment of the probability distribution for the uniaxial anisotropy, and k is the Boltzmann constant. For the Ising model (Δ0=1), there is a spin-glass phase at low temperatures (high J) and a paramagnetic phase at high temperatures (low J). For the isotropic Heisenberg model (Δ0=0), our results indicate no spin-glass phase at finite temperatures. The transition temperature between the spin-glass and paramagnetic phase decreases with Δ0, as expected, but goes to zero at a finite value of the anisotropy parameter, namely Δ0 = Δc ∼ 0.59. Our results indicate that the whole transition line, between the paramagnetic and the spin-glass phases, for Δc ≤ Δ0 < 1, belongs to the same universality class as the transition for the Ising spin glass.